Chapter 4: Q. 4.110 (page 517)

Use slopes to determine if the lines $y = 2 x - 5$ and $x + 2 y = - 6$ are perpendicular.

Short Answer

Expert verified

The slopes are negative reciprocals of each other, so the lines are perpendicular.

Step by step solution

Step 1. Given information.

The given equations are:

$\begin{array}{rcl} y & = & 2 x - 5 \\ x + 2 y & = & - 6 \end{array}$

Step 2. Write the equations in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where m is the slope and $(0, b)$ is the y-intercept.

The first equation is already in slope-intercept form.

The second equation can be written as:

$\begin{array}{rcl} 2 y & = & - x - 6 \\ y & = & \frac{- x - 6}{2} \\ y & = & - \frac{1}{2} x - 3 \end{array}$

Step 3. Determine the slopes.

Compare the slope intercepts forms of the equations with $y = m x + b$ .

For the first equation, $m_{1} = 2$ .

For the second equation, $m_{2} = - \frac{1}{2}$ .

Step 4. Determine whether the lines are perpendicular or not.

If the product of slopes is $- 1$ , then the lines are perpendicular.

$\begin{array}{rcl} m_{1} \cdot m_{2} & = & 2 \cdot (- \frac{1}{2}) \\ = & - 1 \end{array}$

The slopes are negative reciprocals of each other, so the lines are perpendicular.

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Use slopes to determine if the lines $y = 2 x - 5$ and $x + 2 y = - 6$ are perpendicular.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the equations in slope-intercept form.

Step 3. Determine the slopes.

Step 4. Determine whether the lines are perpendicular or not.

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Use slopes to determine if the lines y=2x-5and x+2y=-6are perpendicular.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the equations in slope-intercept form.

Step 3. Determine the slopes.

Step 4. Determine whether the lines are perpendicular or not.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Applied Mathematics

Decision Maths

Geometry

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Use slopes to determine if the lines $y = 2 x - 5$ and $x + 2 y = - 6$ are perpendicular.