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Exercises Graphs and straight lines

Example 19 from Algebra and Trigonometry, 4.1 Linear Functions

Finding a Line Parallel to a Given Line

Find a line parallel to the graph of $f (x) = 3 x + 6$ that passes through the point $(3, 0) .$

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
The slope of the given line is 3. If we choose the slope-intercept form, we can substitute $m = 3, x = 3,$ and $f (x) = 0$ into the slope-intercept form to find the y-intercept.
$\begin{matrix} g (x) & = & 3 x + b \\ 0 & = & 3 (3) + b \\ b & = & –9 \end{matrix}$
The line parallel to $f (x)$ that passes through $(3, 0)$ is $g (x) = 3 x - 9.$

How did it go?

PreviousIdentifying Parallel and Perpendicular Lines Next Finding the Equation of a Perpendicular Line

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 4.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.