Write an equation that represents the line?

Question

asked Nov 6, 2022 34.9k views

1 Answer

RobCo · Answer 1 · 2022-11-10T13:41:12+0000

Answer:

An equation that represents the line is:

y = 3/4x - 9/2

Explanation:

The slope-intercept form of the line equation

y = mx+b

where

Given the attached graph of a line.

Taking two points from the line, such as

Determining the slope between (2, -3) and (0, 6)

$\left(x_1,\:y_1\right)=\left(2,\:-3\right),\:\left(x_2,\:y_2\right)=\left(6,\:0\right)$

$m=(0-\left(-3\right))/(6-2)$

refine

m=(3)/(4)

substituting m = 3/4 and the point (2, -3) in the slope-intercept form of the line equation

y = mx + b

$\left(-3\right)=(3)/(4)\left(2\right)+b$

(3)/(2)+b=-3

subtract 3/2 from both sides

(3)/(2)+b-(3)/(2)=-3-(3)/(2)

b=-(9)/(2)

now substituting b = -9/2 and m = 3/4 in the slope-intercept form of the line equation

y = mx + b

y = 3/4x + (-9/2)

Therefore, an equation that represents the line is:

y = 3/4x - 9/2