Answer:
Equation of line is
[tex]y = -8x - 16[/tex]
Step-by-step explanation:
The equation of a line in slope-intercept form is
[tex]y = mx + b[/tex]
where
[tex]m = $ slope $= \dfrac{y2 - y1}{x2 - x1}\\where (x1, y1) and (x2, y2) are two points on the line[/tex]
b = y-intercept (value of y at x = 0)
Since the line passes through [tex](3, -40) $ and $(1, -24),[/tex]
[tex]m = \dfrac{-24 - -40}{1 - 3}[/tex]
[tex]m = \dfrac{-24 + 40}{-2}[/tex]
[tex]m = \dfrac{16}{-2}[/tex]
[tex]m = - 8[/tex]
The equation of the line is:
[tex]y = -8x + b[/tex]
To find b substitute x, y values for any of the given points and solve for b
Choose point [tex](1, -24)[/tex]
[tex]-24 = -8(1) + b[/tex]
[tex]-24 = -8 + b[/tex]
[tex]-24 + 8 = b[/tex]
[tex]-16 = b[/tex]
[tex]b = -16[/tex]
So the equation of the line is
[tex]y = -8x - 16[/tex]