Question 244092: Find the equation for each of the following items below:
a. A line that passes through (6,2) and has a slope of 2.
b. A line that passes though the points (2,4) and (8,16)
c. A line that passes through (7,3) and has a slope of -1.
d. A line that passes through (1, 1) and is perpendicular to the line 3x+4Y=12.
e. A circle with a radius of 9 and a midpoint at (3,3)
Found 2 solutions by solver91311, checkley77:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
First thing: You cannot find (or write) "the" equation of a line. There are an infinity of equivalent representations of any line, hence the best you can do is find "an" equation of a line.
If you are given a point and the slope, then use the point-slope form of a line:
 )
Where  is the given slope and ) is the given point.
If you are not given the slope directly, but are given that the desired line is either parallel or perpendicular to a given line, use one of the following to determine the slope:
If you are given two points, you can either compute the slope using the slope formula,
Where and ) are the coordinates of the given points
And then use the point-slope form as above, or you can use the two-point form of a line:
(x - x_1) )
Which is really nothing more than a combination of computing the slope and writing the equation.
In all cases, you should determine, either from the instructions in your text or from your instructor's guidance, what form your answers should take. Generally, it is one of two forms that are specified, if any:
1. Slope-intercept form:  where is the slope and ) is the point of intersection of the line with the  -axis.
2. Standard form:  Some text require  ,  , and  to be integers for proper standard form.
A circle centered at ) and with radius  is described by:
^2 + (y - k)^2 = r^2)
Since you were given the center and a point on the circle, you will have to calculate the radius by using the distance formula to determine the distance from the center to the given point.
^2 + (y_1 - y_2)^2})
Again where and are the coordinates of the given points.
John
Answer by checkley77(12844)  (Show Source):
You can put this solution on YOUR website! Y=mX+b where m=slope & b=the y intercept.
a. A line that passes through (6,2) and has a slope of 2.
2=2*6+b
2=12+b
b=2-12
b=-10 The Y intercept.
Y=2X-10 ans.
b. A line that passes though the points (2,4) and (8,16)
slope=(Y2-Y1)/(X2-X1)=(16-4)/(8-2)=12/6=2
4=2*2+b
4=4+b
b=4-4
b=0 The Y intercept.
Y=2X ans.
c. A line that passes through (7,3) and has a slope of -1.
3=-1*7+b
3=-7+b
b=1+7
b=8 The Y intercept.
Y=-X+8 ans.
d. A line that passes through (1, 1) and is perpendicular to the line 3x+4Y=12.
3X+4Y=12
4Y=-3X+12
Y=-3X/4+12/4
Y=-3X/4+3 This line has a slope=-3/4. A perpendicular line will havwe a
slope=4/3.
1=4/3*1+b
1=4/3+b
b=1-4/3
b=-1/3 The Yintercept.
e. A circle with a radius of 9 and a midpoint at (3,3)
(X-3)^2+(Y-3)^2=9^2
I tried to graph this circle using the graphing formula, but could not draw the circle.
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