Question

Write an equation that represents the line?

Answer 1

Answer:

An equation that represents the line is:

y = 3/4x - 9/2

Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

where

• m is the slope

• b is the y-intercept

Given the attached graph of a line.

Taking two points from the line, such as

• (2, -3)

• (6, 0)

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

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

$m=\frac{0-\left(-3\right)}{6-2}$

refine

$m=\frac{3}{4}$

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

y = mx + b

$\left(-3\right)=\frac{3}{4}\left(2\right)+b$

$\frac{3}{2}+b=-3$

subtract 3/2 from both sides

$\frac{3}{2}+b-\frac{3}{2}=-3-\frac{3}{2}$

$b=-\frac{9}{2}$

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