Question

Find the equation of the line through the points (-2,-8) and (3,2).Enter your answer in slope-intercept form y=mx+b.

Answer 1

To determine the equation of the line, given that you know two points of the line, the first step is to calculate the slope of the line.

Use the formula of the slope:

`m=(y_2-y_1)/(x_2-x_1)`

Where

(x₁,y₁) are the coordinates of one point of the line

(x₂,y₂) are the coordinates of a second point of the line

Use (-2,-8) as (x₁,y₁) and (3,2) as (x₂,y₂)

`\begin{gathered} m=(2-(-8))/(3-(-2)) \\ m=(2+8)/(3+2) \\ m=(10)/(5) \\ m=2 \end{gathered}`

The slope of the line is m=2

Next, using the point-slope form, you can determine the equation of the line:

`y-y_1=m(x-x_1)`

Replace (-2,-8) as (x₁,y₁) and m=2

`\begin{gathered} y-(-8)=2(x-(-2)) \\ y+8=2(x+2) \end{gathered}`

Next, write the equation in slope-intercept form:

Distribute the multiplication in the parentheses term

`\begin{gathered} y+8=2\cdot x+2\cdot2 \\ y+8=2x+4 \end{gathered}`

Subtract 8 from both sides of the equal sign

`\begin{gathered} y+8-8=2x+4-8 \\ y=2x-4 \end{gathered}`

So, the equation of the line is y=2x-4