Question

Complete the equation of the line through (2,-2)(2,−2)left parenthesis, 2, comma, minus, 2, right parenthesis and (4,1)(4,1)left parenthesis, 4, comma, 1, right parenthesis. Use exact numbers.

Answer 1

y= 3/2 x -5

Explanation:

khan academy :)

Answer 2

`y=(3)/(2)x-5`

Explanation:

There are a couple of ways to solve this, depending on what you already know.

Point-Slope Form

`y-y_1=m(x-x_1)` where m is the slope and
`(x_1, y_1)` is a point on the line.

First, calculate the slope using the two given points
`(x_1, y_1), (x_2, y_2)`.

`m=(y_2-y_1)/(x_2-x_1)=(1-(-2))/(4-2)=(3)/(2)` .

Fill in the point-slope pattern

`y-(-2)=(3)/(2)(x-2) \\ y+2=(3)/(2)x-3 \\ y=(3)/(2)x-5`

There's the equation in slope-intercept form (
`y=mx+b`).

Slope-Intercept Form

Use
`y=mx+b` directly.

Find the slope just like the above, so
`m=(3)/(2)`.

Now, plug one of the points (either one!) together with m into

`y=mx+b\\-2=(3)/(2)(2)+b \\ -2=3+b \\ b=-5`

Now you know the value of b, so the equation for the line is

`y=(3)/(2)x-5`