Question 936179: Question #1:
? how to plot points (1,8) and (4,-3) on a line. Please provide an graph showing this.
Question #2:
A line passes through the points (-10,-4) and (-1,2). What is the y intercept?
Thank you.
nbnicole87@verizon.net
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Question #1:
how to plot points (1,8) and (4,-3) on a line. Please provide an graph showing this.
you place the points on the graph and then draw a straight line between them.
the point (1,8) has the x-coordinate of 1 and the y-coordinate of 8.
draw an imaginary vertical line at x = 1.
draw an imaginary horizontal line at y = 8
the intersection of the vertical and horizontal line is the point (1,8).
the other point is found in a similar manner.
you can draw the line manually, but if you want computer software to generate the graph for you, you need to tell the computer software the equation of the line.
the slope intercept form of the equation of a straight line is:
y = mx + b
m is the slope and b is the y-intercept.
from the two points, you can find the slope by using the slope formula of:
m = slope = (y2-y1) / (x2-x1)
(x1,y1) is one of your points.
(x2,y2) is the other of your points.
it doesn't matter which one is which.
i'll assign (1,8) to (x1,y1)
i'll assign (4,-3) to (x2,y2)
(y2-y1) / (x2-x1) becomes (-3-8)/(4-1) which becomes -11/3.
that's your slope.
the general form of the slope intercept form of the equation of a straight line becomes:
y = (-11/3) * x + b
use any one of the points to solve for b.
just replace y with the y-coordinate of the point and replace x with the x-coordinate of the point and solve for b.
i'll use the point (1,8).
y = (-11/3)*x + b becomes 8 = (-11/3)*1 + b
simplify to get:
8 = -11/3 + b
add 11/3 to both sides of the equation to get:
8 + 11/3 = b
since 8 is equivalent to 24/3, this becomes:
24/3 + 11/3 = b
simplify to get:
35/3 = b
the equation of your straight line is:
y = (-11/3)*x + 35/3
the slope is -11/3
the y-intercept is 35/3
that's the equation you put in your graphing software so it can generate the graph for you.
the graph of the equation looks like this:
the y-intercept is the value of y when x is equal to 0.
it is showing as 11.667 which is the decimal equivalent of 35/3.
Question #2:
A line passes through the points (-10,-4) and (-1,2). What is the y intercept?
plot the points on the graph and then draw a straight line between them and extending further out until the line crosses the y-axis.
you should be able to see that the y-intercept is somewhere between y = 2 and 3.
that's you're y-intercept.
if you want to find the exact value, then you need to solve the equation of the line.
that will give you a more exact figure.
slope intercept form of the equation of a straight line is:
y = mx + b
m is the slope and b is the y-intercept.
from the two points, you can find the slope by using the slope equation of:
m = slope = (y2-y1)/(x2-x1)
you can assign either one of the points to (x1,y1) and the other point to (x2,y2)
i'll assign (-10,-4) to (x1,y1) and (-1,2) to (x2,y2)
m = slope = (y2-y1) / (x2-x1) = (2--4)/(-1--10) = (2+4)/(-1+10) = 6/9 = 2/3.
your equation becomes y = 2/3*x + b
now you have to solve for the y-intercept, which is b.
replace x and y with the value of one of the points and then solve for b.
i'll use (-10,-4)
y = 2/3 * x + b becomes -4 = 2/3 * (-10) + b
simplify to get -4 = -20/3 + b
add 20/3 to both sides of the equation to get:
-4 + 20/3 = b
since -4 is equivalent to -12/3, the equation becomes:
-12/3 + 20/3 = b
combine like terms to get:
8/3 = b
your equation becomes y = 2/3 * x + 8/3
the y-intercept is 8/3.
the graph of the equation is shown below:
the y-intercept is shown as 2.667 on the graph.
the y-intercept is actually 8/3 which has a decimal equivalent of 2.667 rounded to 3 decimal places.
|
|
|
