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

Answer:

$y=\frac{3}{2}x-5$

Step-by-step 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 $(x_1, y_1), (x_2, y_2)$.

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(-2)}{4-2}=\frac{3}{2}$ .

Fill in the point-slope pattern

$y-(-2)=\frac{3}{2}(x-2) \\ y+2=\frac{3}{2}x-3 \\ y=\frac{3}{2}x-5$

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 $m=\frac{3}{2}$.

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

$y=mx+b\\-2=\frac{3}{2}(2)+b \\ -2=3+b \\ b=-5$

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

$y=\frac{3}{2}x-5$