Question

A line includes the points (3,8) and (4,10). What is its equation in slope-intercept form? Write your answer using integers, proper fractions, and improper fractions in simplest form

Answer 1

The slope-intercept form of a line is:

`y=mx+b`

Where m is the slope of the line and b is the y-intercept.

As a middle step, we can use the slope-point form, which is:

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

Where (x₁, y₁) is a point in the line.

The slope can be found by using both points:

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

So, using the points we have, (3, 8) and (4, 10):

`m=(10-8)/(4-3)=(2)/(1)=2`

And the slope-point form:

`y-8=2(x-3)`

Now, we can just solve of y to get it to the slope-intercept form:

`\begin{gathered} y-8=2(x-3) \\ y-8=2x-6 \\ y=2x-6+8 \\ y=2x+2 \end{gathered}`

So, the slope-intercept equation is:

`y=2x+2`