Question

Write an equation in slope intercept form that passes through the points (-4,3) and (0,2)

Answer 1

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

Explanation:

Slope-intercept form: y = mx + b

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

Given points: (-4, 3), (0, 2)

(0, 2) = (x1, y1)

(-4, 3) = (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 formula used to find slope:

`(3-2)/(-4-0)`

Simplify:

3 - 2 = 1

-4 - 0 = -4

`(1)/(-4)= -(1)/(4)`

The slope is
`-(1)/(4)`.

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 = -(1)/(4) (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 = -(1)/(4)x +2`