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

Question

2 months ago

15

parenthesis, 4, comma, 1, right parenthesis. Use exact numbers.

1 answer:

Leona [12.6K] · Answer 1 · 2026-03-16T07:52:39+03:00

Response:

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

Detailed explanation:

There are multiple methods to approach this, depending on your existing knowledge.

Point-Slope Formula

$y-y_1=m(x-x_1)$ where m signifies the slope and $(x_1, y_1)$ represents a point along the line.

Initially, determine the slope by utilizing the two provided points $(x_1, y_1), (x_2, y_2)$ .

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

Next, apply the point-slope template

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

This results in the equation formatted in slope-intercept style ( $y=mx+b$ ).

Slope-Intercept Format

Directly use $y=mx+b$ .

Determine the slope as previously described, leading to $m=\frac{3}{2}$ .

Subsequently, insert one of the points (either will suffice!) along with m into

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

After that, you'll ascertain the value of b, thus your equation for the line is

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