Example 6 from Precalculus, 2.1 Linear Functions

Writing Linear Equations Using Two Points

Write the point-slope form of an equation of a line that passes through the points (5, 1) and (8, 7). Then rewrite it in the slope-intercept form.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Let’s begin by finding the slope.

$\begin{array}{l} \begin{array}{l} m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \end{array} \\ = \frac{7 - 1}{8 - 5} \\ = \frac{6}{3} \\ = 2 \end{array}$
So $m = 2.$ Next, we substitute the slope and the coordinates for one of the points into the general point-slope equation. We can choose either point, but we will use $(5, 1) .$

$\begin{matrix} y - y_{1} = m (x - x_{1}) \\ y - 1 = 2 (x - 5) \end{matrix}$

The point-slope equation of the line is $y_{2} - 1 = 2 (x_{2} - 5) .$ To rewrite the equation in slope-intercept form, we use algebra.

$\begin{array}{l} y - 1 = 2 (x - 5) \\ y - 1 = 2 x - 10 \\ y = 2 x - 9 \end{array}$
The slope-intercept equation of the line is $y = 2 x - 9.$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Write the point-slope form of an equation of a line that passes through the points $(–1, 3)$ and $(0, 0) .$ Then rewrite it in the slope-intercept form.

How did it go?

Solution

Your turn

Solution

Your turn