Question

Write an equation that represents the line?

Answer 1

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

• 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=(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