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Chapter 1: Q. 9 (page 40)

The lines $y = 2 x - 1$ and $y = a x + 2$ are perpendicular if $a =$ ____.

Short Answer

Expert verified

The lines $y = 2 x - 1$ and $y = a x + 2$ are perpendicular if $a = - \frac{1}{2}$ .

Step by step solution

01

Step 1. Given information.

We have two equation:

$y = 2 x - 1 y = a x + 2$

02

Step 2. Fill the blank.

Two non-vertical lines are perpendicular if and only if the product of their slopes is $- 1 .$

Comparing the two equation with slope intercept form $y = m x + b$ , we get:

$m_{1} = 2 m_{2} = a$

Since two lines are perpendicular, we get:

$m_{1} \times m_{2} = - 1 2 \times a = - 1 a = - \frac{1}{2}$

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Most popular questions from this chapter

The figure shows the graph of two parallel lines. Which of the following pairs of equations might have such a graph?

$(a) x - 2 y = 3 x + 2 y = 7 (b) x + y = 2 x + y = - 1 (c) x - y = - 2 x - y = 1 (d) x - y = - 2 2 x - 2 y = - 4 (e) x + 2 y = 2 x + 2 y = - 1$

The figure shows the graph of two perpendicular lines. Which of the following pairs of equations might have such a graph?

$(a) y - 2 x = 2 y + 2 x = - 1 (b) y - 2 x = 0 2 y + x = 0 (c) 2 y - x = 2 2 y + x = - 2 (d) y - 2 x = 2 x + 2 y = - 1 (e) 2 x + y = - 2 2 y + x = - 2$

Find the midpoint of the line segment joining the points P₁ and P₂ .

$P_{1} = (- 4, - 3); P_{2} = (2, 2)$

Find the length of the line segment. Assume that the endpoints of each line segment have integer coordinates.

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

$\frac{x + 1}{3} + \frac{x + 2}{7} = 5$

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