Q. 16 - Precalculus Enhanced with Graphing Utilities

Question

Find the slope-intercept form of the equation of the line containing the points $\left(-2,4\right),\left(6,8\right)$.

Step-by-Step Solution

Answer

The slope-intercept form is $y=\frac{1}{2}x+5$.

Step 1. Given information.

Consider the given question,

$\left(-2,4\right),\left(6,8\right)$

Slope of the formula,

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

Substitute the values,

$$\begin{gathered} m=\frac{8-4}{6-\left(-2\right)} \\ =\frac{4}{8} \\ =\frac{1}{2} \end{gathered}$$

Step 2. Find the point-slope form.

We know the point-slope form,

$y-y_1=m\left(x-x_1\right)$

Substitute the values,

$$\begin{gathered} y-8=\frac{1}{2}\left(x-6\right) \\ y-8=\frac{1}{2}x-3 \\ y=\frac{1}{2}x-3+8 \\ y=\frac{1}{2}x+5 \end{gathered}$$