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Exercises Equations and inequalities

Example 15 from Algebra and Trigonometry, 2.2 Linear Equations in One Variable

Writing the Equation of a Line Parallel to a Given Line Passing Through a Given Point

Write the equation of line parallel to a $5 x + 3 y = 1$ and passing through the point $(3, 5) .$

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
First, we will write the equation in slope-intercept form to find the slope.

$\begin{matrix} 5 x + 3 y & = & 1 \\ 3 y & = & –5 x + 1 \\ y & = & - \frac{5}{3} x + \frac{1}{3} \end{matrix}$
The slope is $m = - \frac{5}{3} .$ The y-intercept is $\frac{1}{3},$ but that really does not enter into our problem, as the only thing we need for two lines to be parallel is the same slope. The one exception is that if the y-intercepts are the same, then the two lines are the same line. The next step is to use this slope and the given point with the point-slope formula.

$\begin{matrix} y - 5 & = & - \frac{5}{3} (x - 3) \\ y - 5 & = & - \frac{5}{3} x + 5 \\ y & = & - \frac{5}{3} x + 10 \end{matrix}$
The equation of the line is $y = - \frac{5}{3} x + 10.$ See Figure 7.

Figure 7

Your turn

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

Find the equation of the line parallel to $5 x = 7 + y$ and passing through the point $(−1, −2) .$

How did it go?

PreviousGraphing Two Equations, and Determining Whether the Lines are Parallel, Perpendicular, or Neither Next Finding the Equation of a Line Perpendicular to a Given Line Passing Through a Given Point

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 2.2, 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.