Answer:
a. Slope = -4/3
b. y-intercept = -5
c. Equation: y = -4/3x -5
Explanation:
a.
First, we find the slope of the line connecting the two points
[tex]slope=\frac{\Delta y}{\Delta x}=\frac{3--1}{-6+3}=-\frac{4}{3}[/tex]
b.
We know that the slope-intercept of a line is
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
Since m = -4/3, we have
[tex]y=-\frac{4}{3}x+b[/tex]
from (-3, -1) we know that when y = -1, x = -3 and so putting these values in the abvoe equation gives
[tex]-1=-\frac{4}{3}(-3)+b[/tex][tex]\rightarrow-1=4+b[/tex]
subtracting 4 form both sides gives
[tex]b=-5[/tex]
Hence the y-intercept is -5.
c.
The equation of the line is (with m = -4/3 and b = -5)
[tex]y=-\frac{4}{3}x-5[/tex]
which is our answer!
