Question

Which of the following equations describes the line shown below ?

Answer 1

Given:

Points on the line are (-2, 4) and (-4, -8).

To find:

The equation of a line.

Solution:

`x_1=-2, y_1=4, x_2=-4, y_2=-8`

Slope of the line:

`$m=(y_2-y_1)/(x_2-x_1)`

Substitute the given points.

`$m=(-8-4)/(-4-(-2))`

`$m=(-12)/(-4+2)`

`$m=(-12)/(-2)`

m = 6

Point-slope formula:

`y-y_1=m(x-x_1)`

Substitute
`x_1=-2, y_1=4` and m = 6

`y-4=6(x-(-2))`

y - 4 = 6(x + 2)

Substitute
`x_1=-4, y_1=-8` and m =6 in point-slope formula.

`y-(-8)=6(x-(-4))`

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.