Example 5 from Precalculus, 2.1 Linear Functions

Writing Linear Equations Using a Point and the Slope

Write the point-slope form of an equation of a line with a slope of 3 that passes through the point $(6, –1) .$ 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 figure out what we know from the given information. The slope is 3, so $m = 3.$ We also know one point, so we know $x_{1} = 6$ and $y_{1} = −1.$ Now we can substitute these values into the general point-slope equation.

$\begin{array}{l} y - y_{1} = m (x - x_{1}) \\ y - (- 1) = 3 (x - 6) & Substitute known values . \\ y + 1 = 3 (x - 6) & Distribute - 1 to find point-slope form . \end{array}$
Then we use algebra to find the slope-intercept form.

$\begin{array}{l} y + 1 = 3 (x - 6) \\ y + 1 = 3 x - 18 & Distribute 3 . \\ y = 3 x - 19 & Simplify to slope-intercept form . \end{array}$

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 with a slope of $–2$ that passes through the point $(–2, 2) .$ Then rewrite it in the slope-intercept form.

How did it go?

Solution

Your turn

Solution

Your turn