Question

Passes through (-2, 1) and (2, -5)

Answer 1

The equation of the line is:

`y = -(3)/(2)x - 2`

Explanation:

Equation of a line:

The equation of a line has the following format:

`y = mx + b`

In which m is the slope and b is the y-intercept.

Slope:

We have two points, (-2,1) and (2,-5). The slope is given by the change in y divied by the change in x. So

Change in y: -5 - 1 = -6

Change in x: 2 - (-2) = 2 + 4 = 4

Slope:
`m = (-6)/(4) = -(3)/(2)`

So

`y = -(3)/(2)x + b`

Passes through (-2, 1)

This means that when
`x = -2, y = 1`. We use this to find the y-intercept. So

`y = -(3)/(2)x + b`

`1 = -(3)/(2)(-2) + b`

`1 = 3 + b`

`b = -2`

So, the equation of the line is:

`y = -(3)/(2)x - 2`