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Exercises Graphs and straight lines

Example 4.56 from Elementary Algebra, 4.5 Use the Slope–Intercept Form of an Equation of a Line

Use the Slope–Intercept Form of an Equation of a Line: example 4.56

Use slopes to determine if the lines, $7 x + 2 y = 3$ and $2 x + 7 y = 5$ are perpendicular.

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

Solve the equations for $y$ . $\begin{matrix} 7 x + 2 y & = & 3 \\ 2 y & = & −7 x + 3 \\ \frac{2 y}{2} & = & \frac{−7 x + 3}{2} \\ y & = & - \frac{7}{2} x + \frac{3}{2} \end{matrix}$ $\begin{matrix} 2 x + 7 y & = & 5 \\ 7 y & = & −2 x + 5 \\ \frac{7 y}{7} & = & \frac{−2 x + 5}{7} \\ y & = & - \frac{2}{7} x + \frac{5}{7} \end{matrix}$

Identify the slope of each line. $\begin{matrix} y & = & m x + b \\ m_{1} & = & - \frac{7}{2} \end{matrix}$ $\begin{matrix} y & = & m x + b \\ m_{2} & = & - \frac{2}{7} \end{matrix}$

Table 4.45

The slopes are reciprocals of each other, but they have the same sign. Since they are not negative reciprocals, the lines are not perpendicular.

Your turn

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

Use slopes to determine if the lines $5 x + 4 y = 1$ and $4 x + 5 y = 3$ are perpendicular.

How did it go?

PreviousUse the Slope–Intercept Form of an Equation of a Line: example 4.55 Next Find the Equation of a Line: example 4.57

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 4.5, 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.