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:

$m=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{10-8}{4-3}=\frac{2}{1}=2$

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:

$y=2x+2$