Question

What is the Slope Intercept equation for the line that passes through the points (2,1) (-4,-2)?

Answer 1

`y=(1)/(2)x`

Explanation:

Slope-intercept form: y = mx + b

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

Given points: (2, 1), (-4, -2)

(2, 1) = (x1, y1)

(-4, -2) = (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:

`(-2-1)/(-4-2)`

Simplify:

-2 - 1 = -3

-4 - 2 = -6

`(-3)/(-6) =(1)/(2)`

The slope is
`(1)/(2)`. We can input the slope and one of the given points (in this example I'll use point (2, 1)) into the equation to find b:

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

1 = 1 + b

0 = b

The y-intercept is 0. Now that we know the slope and the y-intercept, we can write the equation:

`y = (1)/(2)x+0`

`y=(1)/(2)x`