
Tutors Answer Your Questions about Coordinatesystem (FREE)
Question 994328: let f(x)=(1/2)X^23X+(5/2)
a. y intercept
b. x intercept
c. axis of symmetry
d. vertex
f. sketch
THANK YOU!!!
Answer by Fombitz(25151) (Show Source):
Question 994575: what is the vertex of y=(x+2)2squared + 10 ?
Found 2 solutions by MathTherapy, josgarithmetic: Answer by MathTherapy(4047) (Show Source): Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! Write it this way:
y=(x+2)^2+10
The rendering tags will make it look like it should:
This is in standard form. Read the vertex from the equation.
(2,10)
Question 994534: I can not figure this problem out can someone help pls
Natalie performs a chemistry experiment where she records the temperature of an ongoing reaction. The solution is 93.5º C after 3 minutes; 90º C after 5 minutes, 84.8 C after 9 minutes; 70.2º C after 18 minute; 54.4º C after 30 minutes; 42.5ºC after 37 minutes; and 24.9º C after 48 minutes. Perform a linear regression on this data to complete the following items.
Write the equation of the bestfitting line.
Answer by MathLover1(11324) (Show Source):
Question 994417: How do I graph the vertex and axis of : f(x)=(x+3)
plus it said something about symmetry?????
Answer by josgarithmetic(13975) (Show Source):
Question 992589: Find a formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector ℓ of segment AB.
A(−4, 7), B(8, −13)
Answer by anand429(129) (Show Source):
Question 993809: The points (5,3) and (14,8) form the endpoints of a diameter of a circle in the xyplane. Find the xintercepts of the circle. Please help, a stepbystep explanation would be appreciated as I need to ensure that I understand how to solve for these types of problems. Thank you!
Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! Standard Form equation for a circle is . The midpoint of the two given points is the center of the circle. This center will be the point (h,k). The distance using the Distance Formula between (h,k) and either of the two given endpoints gives you your radius, r.
Question 993810: The points (2,7) and (8,3) are equidistant to a point P on the yaxis. Find this point P. Stepbystep explantions are greatly appreciated so I can throughly understand how to solve for these types of problems. Thank you in advance!
Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! The point P on the yaxis would be some ordered pair (0,y) and you want to solve for y. The initial equation uses The Distance Formula.
The points (2,7) and (8,3) are equidistant to a point P on the yaxis.
Simplify and solve for y.
Question 993811: Find an equation for the line that is tangent to the circle x^2+y^2=169 at the point (5,12).
I need help beind reminded of the equation of a circle and equations related to this, and also a stepbystep explantion to help me to understand how to solve this typ of problems and others efficiently. Thank you so much!
Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! Center of circle on the Origin, , and for this, radius is r.
You have , so the radius .
The point ON THE CIRCLE, (5,12), is part of a tangent line which passes through this point. This means, you want to find an equation for this line and this line TOUCHES the circle at this point; and it is perpendicular to the line which contains this point (5,12) and the Origin (which is center of your circle.)

Work to understand that discussion before continuing.
What is the line containing the circle's center (0,0) and the given point (5,12)? You should find just intuitively this is . The yintercept and the xintercept both 0.
What is the equation for the line PERPENDICULAR to and contains the point (5,12)? For perpendicularity, its slope must be negative reciprocal of , so this slope needed will be . You can use the pointslope equation form (for convenience if you are comfortable with it), and plugin the needed slope and included point (5,12):
Use simple algebra if you want this equation in standard form or in slopeintercept form.

Try to make a sketch or a graph on your own to help analyze the problem description.
Question 993691: If the points (2,5) are shifted 5 units up and 4 units down what are the new coordinates
Answer by fractalier(2141) (Show Source):
You can put this solution on YOUR website! Not sure you typed the problem correctly, but if you did
Shifting the point up increases the ycoordinate and shifting it
down decreases the ycoordinate, thus
(2,5) becomes (2,10) and then (2,6).
Question 993535: please help me to sketch the graph of y=5x+ 8
Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! The equation is in slopeintercept form and represents a line. The yintercept is (0,8) and the slope is 5, meaning vertical change is 5 units for every 1 unit of horizontal change.
Question 993428: Show that the points A (1,1),B (3,4), and C (4,1) are the vertices of a right triangle.
Answer by Cromlix(3061) (Show Source):
You can put this solution on YOUR website! Hi there,
Using gradients:
AB = y2  y1/x2  x1
AB = 4(1)/3(1)
AB = 5/2
AB = 5/2
BC = y2  y1/x2  x1
BC = 1  4/4(3)
BC = 3/7
AC = y2  y1/x2  x1
AC = 1 (1)/4(1)
AC = 2/5
Lines that are perpendicular
to one another have gradients
that multiply together to give 1
Side AB and side AC's gradients
multiply together to give 1
5/2 x 2/5 = 1
Right angle is at A
Hope this helps :)
Question 992590: Find a formula that expresses the fact that P(x, y) is a distance 7 from the origin.
Describe the set of all such points.
This is a circle of radius
, with a center at
(x, y) =
Answer by Theo(5548) (Show Source):
You can put this solution on YOUR website! x^2 + y^2 = 49
here's the graph of that equation.
the vertex form of the eqaution of a circle is:
(xh)^2 + (yk)^2 = r^2
r is the radius of the circle..
(h,k) is the (x,y) coordinate of the center of the circle.
in your circle, the center is (0,0) so h = 0 and k = 0
in your circle,
any point p(x,y) that lies on the circle, will be r units away from the center of the circle.
here's a reference that might help you understand that better.
https://www.mathsisfun.com/algebra/circleequations.html
they use (a,b) as the center of the circle,
i use (h,k) as the center of the circle.
doesn't matter.
they reference the same thing.
a or h references the xcoordinate of the center of the circle.
b or k references the ycoordinate of the center of the circle.
Question 990836: The lines xy2=0 and 2x5y7=0 intersect at point P. Find coordinates of point P. The line through P with gradient 2 meets the axis A and B. Calculate the area of triangle AOB.
Answer by anand429(129) (Show Source):
You can put this solution on YOUR website! xy2=0 (i)
2x5y7=0 (ii)
Multiplying eqn (i) by 2,
2x2y4=0 (iii)
Subtracting (ii) from (iii), we get,
3y+3=0
=> y = 1
Putting back, x= y+2 = 1
So, intersection pt. P is (1,1)
Let the line through P with gradient 2 be given by,
y = 2x + c
Since it passes through P(1,1)
1 = 2*1 + c
=> c = 3
So the required line is
y = 2x  3
For finding intersection with axes, putting x and y =0 separately, we get, the intersection points as A(0,3) and B(3/2,0)
So, area of triangle OAB
= (1/2)*(3)*(3/2)
= 9/4 sq. units.
Question 992593: Find the point with coordinates of the form (3a, a) that is in the third quadrant and is a distance 5 from
P(1, 2).
(x, y) =
Answer by anand429(129) (Show Source):
Question 992728: Graph each equation using the gradient and yintercept for:
y= 5/2x 3
Answer by Fombitz(25151) (Show Source):
You can put this solution on YOUR website! First plot the yintercept.
(0,3)
Slope is equal to change in y over change in x.
So for a change in x of 2, y changes 5 units.
(0,3)+(2,5)=(2,2)
Plot that point and draw the line.
.
Question 992588: Find all points on the yaxis that are a distance 7 from P(5, 9).
Answer by macston(4006) (Show Source):
Question 992391: FIND FIVE ORDERED PAIRS TO THE EQUATION Y=3x(1)1
Answer by solver91311(20879) (Show Source):
You can put this solution on YOUR website!
Sorry, we can't understand you when you shout. Turn off caps lock and repost.
John
My calculator said it, I believe it, that settles it
Question 992219: x^2+y^2+6x6y107=0 What is the Radius and Center of a circle
Answer by Alan3354(47455) (Show Source):
Question 992124: find the equation which is parallel and perpendicular to 2y+3x4=0
Answer by ikleyn(988) (Show Source):
You can put this solution on YOUR website! .
Straight line 4y + 6x  4 = 0 is parallel to the original straight line 2y + 3x  4 = 0.
Straight line 2x  3y = 0 is perpendicular to the original straight line 2y + 3x  4 = 0.
Question 991586: If f(−4)=−1, write an ordered pair that must be on the graph of y=f(x−5)+2
Answer by ikleyn(988) (Show Source):
You can put this solution on YOUR website! .
This ordered pair is
(x,y) = (1, 1).
I.e. x=1 and y=1.
Indeed, if you substitute x=1 into f(x5), you will get f(15) = f(4), which is 1 by the condition.
Hence, f(x5)+2 = 1 + 2 = 1, which is the value of y in the pair.
Question 991540: An airplane travels 3035km against the wind in 5 hours and 3935km with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! Same problem, different numbers.
==============================================
an airplane, flying with a tail wind, travels 2000 miles in five hours. The return trip, against the wind, takes eight hours. Find the cruising speed of the plane and the speed of the wind (assuming that both rates are constant)
==================
find the 2 groundspeeds, downwind and upwind.
The plane's airspeed is the average of the 2.

Windspeed = difference between airspeed and groundspeed.
Question 989964: For what value of m will the triangle formed by the lines y=5, y=mx6 and
y=mx6 be equilateral?
Answer by Fombitz(25151) (Show Source):
Question 989944: Use given endpoint "r" and midpoint "m".find s in rs segment. R=6.2. M=5.3
Answer by Fombitz(25151) (Show Source):
Question 990981: Express this in general form: Slope: 2/7 containing the point (4,7)
Answer by josgarithmetic(13975) (Show Source):
Question 990894: Can you please help find the x and y coordinates of 6x+3y=12
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! Can you please help find the x and y coordinates of 6x+3y=12
==============
The graph of 6x + 3y = 12 is a line of infinite length.
Every point on it has an (x,y) pair.

6x + 3y = 12
y = 2x + 4

Pick any value of x and find y.
eg,
x = 0 > y = 4 > (0,4)
x = 1 > y = 6 > (1,6)
etc
Question 990626: explain in detail please: find all points having an x coordinate of 2 whose distance from the point (2,1) is 5.
Answer by josgarithmetic(13975) (Show Source):
Question 990623: hello, this is my homework and I couldn't find the right answer for it. I will provide the step I did to try and solve the problem. Also, I would really appreciate if you could point out the mistake I did so I could improve.
Question:
Find the point (x,y) on the line y=−2x−3 that is equidistant from the points (−1,6) and (−2,9).
my step:
d² = (xa)² + (xb)²
= (x[1])² + (y6)²
= x² +2x+1+y²12y+36=x²+4x+4+y²18y+81
2x+112y+364x4+18y81=0
2x+6y48=0
2x+6(2x3)48
2x12x1848
14x66
x=66/14
y=2x3
= 2(66/14)3
= 174/14
Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! You have an unknown line with general points, (x, 2x3). This point is same distance from point (1,6) as from point (2,9).
Distance Formula will give the equation to express that reworded description.
Analyze that for it to all make sense. You can then continue with the algebraic steps to simplify the equation and solve for x.
Question 990503: which of the following combinations represents the vertex and two xintercepts of the function given below? y=x^22x35
Answer by Fombitz(25151) (Show Source):
Question 988854: Find the coordinates of the other endpoint of the segment, given it's midpoint M and one endpoint Q.
M(a,k), Q(f,q)
The second endpoint is P
Answer by Shai(25) (Show Source):
You can put this solution on YOUR website! Let the missing coordinates of the endpoint P be (x,y),
Mid point given :M(a,k) henceforth
a=(x+f)/2,2af
K=(y+q)/2,2kq
The end point P(2af,2kq)
Question 988589: HI, this question is from my textbook.
The equations of two sides of a square are y=3x1 and x+3y6=0. (0,1) is one vertex of the square. Find the coordinates of the other vertices.
Found 2 solutions by KMST, Alan3354: Answer by KMST(3791) (Show Source):
You can put this solution on YOUR website! , and are the equations of two sides of the square.
The coordinates of the vertex at the intersection of those two sides can be found by solving the system
>>>>>>> .
So, point (9/10,17/10), or (0.9,1.7) is one vertex,
the one at the intersection of the two given sides.
Point (0,1) , with is the other end/vertex of that side with equation .
So far we have this:
What we do not know is to what side of segment to draw the square.
There are really two right answers. Which one will be the right one according to your textbook? Or did the authors realize that there were two possible answers?
We can draw the square to the right, like this:
, or we can draw the square to the left, as Alan suggested.
Either way, if we encase that square inside a larger square with sides parallel to the x and yaxes,
we form four congruent right triangles with legs measuring
and , like this
So, , ,
, and .
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! The equations of two sides of a square are y=3x1 and x+3y6=0. (0,1) is one vertex of the square. Find the coordinates of the other vertices.

(0,1) is point A.
Find the intersection of the lines, that's a 2nd vertex, point B.

y=3x1
x+3y6=0 > y = (1/3)x + 2

x + 3(3x1) = 6
10x = 9
x = 0.9, y = 1.7 > B(0.9,1.7)

The distance between the 2 points is the side length.

Find the line thru A(0,1) parallel to x+3y6=0
> y = (1/3)x  1
A vertex (point D) is on this line distance s from point A.
The xdistance from A to D is 2.7, and the ydistance is 0.9
> D (2.7,0.1)

The side CD goes thru D with a slope of 3 (parallel to AB)
y + 0.1 = 3(x + 2.7)
y = 3x + 8

Vertex C is the intersection of y = 3x + 8 and y = (1/3)x + 2
3x + 8 = x/3 + 2
10x/3 = 6
x = 1.8, y = 2.6
C(1.8,2.6)
Question 988580: To make 14 gallons of orange paint, a worker mixes 10 gallons of red paint and 4 gallons of yellow paint, but the color is incorrect. What is the correct combination? What is the likely error that the worker made?
Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! Either wrong recipe (formula) or mistake in using the formula's quantities. Not much more can reasonably be in this response. Anything more depends on having oneself in the practical situation, and having a color reference sample.
Question 987277: Write an equation in standard form for a line with an x intercept of 3 and y intercept of 6
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! Write an equation in standard form for a line with an x intercept of 3 and y intercept of 6
===============
6x + 3y = 18
2x + y = 6
Question 987218: On a graph, there is a point plotted on (1,2) and (3,0).
What is the:
A) Domain
B) Range
C) C) X values of all zeroes
D) Equations of all asymptotes
E) 1 to 1 or not
F) Continuous or not (if continuous tell where)
G) Increasing, decreasing, both (if both tell where), or neither
H) Bounded above, bounded below, bounded, or unbounded (if unbounded, tell where)
Answer by solver91311(20879) (Show Source):
You can put this solution on YOUR website!
Does the function consist only of the two given points, or are these two points on a straight line that represents the function? Or are we just supposed to guess what you are talking about. By the way, which ONE of your myriad of questions to you want answered?
John
My calculator said it, I believe it, that settles it
Question 987210: Draw the graph of:
x/6  y/4 = 1
Found 2 solutions by stanbon, macston: Answer by stanbon(69061) (Show Source):
You can put this solution on YOUR website! Draw the graph of:
x/6  y/4 = 1

Let x = 0, then y = 4
Let y = 0, then x = 6

Plot (0,4) and (6,0) and draw a line thru them

Cheers,
Stan H.

Answer by macston(4006) (Show Source):
Question 987164: Jane goes for a walk.On the map it shows that she walked 5cm.Calculate the actual distance in kilometres she has walked if the scale of the map is 1:15 000.
Answer by Cromlix(3061) (Show Source):
Question 986437: what is the equation of the Vertical line that passes through the points (6,5) and (6,4)
What is the equation of the Horizontal line that passes through the points (5,6) and (4,6)
Answer by mananth(14512) (Show Source):
Question 986230: Y=2x+3
Answer by EdenWolf(454) (Show Source):
Question 985744: Write an equation in slopeintercept form
Perpendicular to y= 3x  2
Passes through (6, 1)
Answer by josgarithmetic(13975) (Show Source):
Question 985204: How do you write an equation in standard form that goes through the point (4,3)
and with a yintercept of 0?
Answer by MathLover1(11324) (Show Source):
You can put this solution on YOUR website! given:
the line passes through the point (,)
and with a yintercept of ; means the line will pass through origin (,)
so, firs we can find the equation of this line in slopeintercept form
Solved by pluggable solver: Find the equation of line going through points 
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (4, 3) and (x2, y2) = (0, 0).
Slope a is .
Intercept is found from equation , or . From that,
intercept b is , or .
y=(0.75)x + (0)
Your graph:

so, the equation of this line in slopeintercept form is
the standard form for linear equations:
so, we have
Question 985086: x=7y what are the ordered pairs
Answer by Alan3354(47455) (Show Source):
Question 985085: x=7y what are the ordered pairs
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! x=7y what are the ordered pairs

Pick values for y and find x.
eg,
y = 0, x = 7 > (7,0)
y = 7, x = 0 > (0,7)
y = 100, x = 93 > (93,100)
etc
Question 984742: Find all points on the xaxis that are 6 units from the point (4,3).
Answer by josgarithmetic(13975) (Show Source):

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645

 