Chapter 4: Q. 666 (page 572)

In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.
Line $y = - \frac{4}{5} x + 2$ , point $(8, 9)$

Short Answer

Expert verified

The equation of the required line is $y = \frac{5}{4} x - 1$ .

Step by step solution

Step 1. Given information.

Consider the given question,

Line $y = - \frac{4}{5} x + 2$ , point $(8, 9)$

Step 2. Find the slope.

Slopes of the perpendicular lines are negative reciprocals of each other. If $m_{1}, m_{2}$ are the slopes of two perpendicular lines then role="math" localid="1647786483562" $m_{2} = - \frac{1}{m_{1}}$ .

We know, the slope intercept form of the line is $y - y_{1} = m (x - x_{1}) . . . . . . (i)$ .

Compare the given line with equation (i),

$m_{1} = - \frac{4}{5}$

Slope of the perpendicular line,

$m_{2} = - (\frac{1}{- \frac{4}{5}}) m_{2} = \frac{5}{4}$

Step 3. Find the equation of the line.

Substituting the values in equation (i),

$y - 9 = \frac{5}{4} (x - 8) y - 9 = \frac{5}{4} x - \frac{5}{4} (8) y - 9 = \frac{5}{4} x - 10 y = \frac{5}{4} x - 1$

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In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.
Line $y = - \frac{4}{5} x + 2$ , point $(8, 9)$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the slope.

Step 3. Find the equation of the line.

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x	y	(x,y)
0
2
-1

In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.Liney=-45x+2, point8,9

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the slope.

Step 3. Find the equation of the line.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Applied Mathematics

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Geometry

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.
Line $y = - \frac{4}{5} x + 2$ , point $(8, 9)$