Question

The graph below shows a line segment AB:

Which of the following equations best represents the line segment AB?
graph of line AB going through ordered pairs negative 1, 5 and 2, negative 4

y = −3x + 2
y = −2x + 1
y = −3x − 2
y = −2x − 1

Answer 1

The correct option is 1.

Explanation:

It is given that the line AB, going through ordered pairs (-1,5) and (2,-4).

If a line passing through two points, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The equation of line AB is

`y-5=(-4-5)/(2-(-1))(x-(-1))`

`y-5=(-9)/(2+1)(x+1)`

`y-5=(-9)/(3)(x+1)`

`y-5=-3(x+1)`

`y-5=-3x-3`

Add 5 both the sides.

`y=-3x+2`

Therefore option 1 is correct.

Answer 2

Equation of a line passing through given two points is given by (y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
(y - 5)/(x - (-1)) = (-4 - 5)/(2 - (-1))
(y - 5)/(x + 1) = -9/(2 + 1) = -9/3 = -3
y - 5 = -3(x + 1) = -3x - 3
y = -3x - 3 + 5
y = -3x + 2