Write the equation of a line that passes through (4, 0) and (-4, -5). Write your answer in slope-intercept form.

Question

Write the equation of a line that passes through (4, 0) and (-4, -5). Write your answer in slope-intercept form. Thank you, Adeline

Answer 1

Hi Adeline;

We first must establish slope.  Slope is defined as change-of-y divided by change-of-x, also known as rise-over-run.

m=(y-y₁)/(x-x₁)

(4, 0) and (-4, -5)

m=(0--5)/(4--4)

Subtracting a negative number is the same as adding a positive number...

m=(0+5)/(4+4)

m=5/8

We will use point-slope formula...

y-y₁=m(x-x₁)

We will select either point.  I randomly choose the second.

y--5=(5/8)(x--4)

y+5=(5/8)(x+4)

y+5=(5/8)x+(20/8)

y+5=(5/8)x+(5/2)

Let's subtract 5 from both sides...

y+5-5=(5/8)x+(5/2)-5

Let's convert 5 into 10/2...

y=(5/8)x+(5/2)-(10/2)

y=(5/8)x-(5/2)

Let's take this equation and input the other coordinate to verify...

y=(5/8)x-(5/2)

(4,0)

0=[(5/8)(4)]-(5/2)

0=(20/8)-(5/2)

(20/8)...we can divide the numerator and denominator by 4 for the result of (5/2)

0=(5/2)-(5/2)