Given:
Points on the line are (-2, 4) and (-4, -8).
To find:
The equation of a line.
Solution:
[tex]x_1=-2, y_1=4, x_2=-4, y_2=-8[/tex]
Slope of the line:
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given points.
[tex]$m=\frac{-8-4}{-4-(-2)}[/tex]
[tex]$m=\frac{-12}{-4+2}[/tex]
[tex]$m=\frac{-12}{-2}[/tex]
m = 6
Point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute [tex]x_1=-2, y_1=4[/tex] and m = 6
[tex]y-4=6(x-(-2))[/tex]
y - 4 = 6(x + 2)
Substitute [tex]x_1=-4, y_1=-8[/tex] and m =6 in point-slope formula.
[tex]y-(-8)=6(x-(-4))[/tex]
y + 8 = 6(x + 4)
Option A and Option D are the correct answers.
Therefore y - 4 = 6(x + 2) and y + 8 = 6(x + 4) are the equations describes the shown line.
