Question

What is the equation of the line that passes through the points (0,-2) and (-4,4)

Answer 1

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

Explanation:

Slope-intercept form: y = mx + b

Slope formula:
`(y2-y1)/(x2-x1)`

Given points: (0, -2), (-4, 4)

(0, -2) = (x1, y1)

(-4, 4) = (x2, y2)

To write the equation in slope-intercept form, we need to find the slope(m) and the y-intercept(b) of the equation.

First, let's find the slope. To do this, input the given points into the slope formula:

`(4-(-2))/(-4-0)`

Simplify:

4 - (-2) = 4 + 2 = 6

-4 - 0 = -4

`(6)/(-4)=-(3)/(2)`

The slope is
`-(3)/(2)`.

To find the y-intercept, input the slope and one of the given points(in this example I'll use point (0, -2)) into the equation and solve for b:

`-2 = -(3)/(2)(0)+b`

-2 = 0 + b

-2 = b

The y-intercept is -2.

Now that we know the slope and the y-intercept, we can write the equation:

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