Question

A line passes through the point (-4, 7) and has a slope of -5/4

Write an equation in slope-intercept form for this line.

Answer 1

We conclude that the equation in slope-intercept form for this line will be:

`y\:=\:(-5)/(4)x+2`

Explanation:

Given

• The point = (-4, 7)

• slope = m = -5/4

We know that the slope-intercept form of the line equation is

`y=mx+b`

where m is the slope and b is the y-intercept

Using the slope-intercept form to find the y-intercept 'b'

substituting m = -5/4 and the point (-4, 7)

`y = mx+b`

`7=\:(-5)/(4)\left(-4\right)+b`

`-\left(-5\right)+b=7`

`5+b=7`

subtract 5 from both sides

`5+b-5=7-5`

`b=2`

now substituting b = 2 and m = -5/4 in the slope-intercept form

`y = mx+b`

`y\:=\:(-5)/(4)x+2`

Therefore, we conclude that the equation in slope-intercept form for this line will be:

`y\:=\:(-5)/(4)x+2`