Chapter 4: Q. 4.133 (page 535)

Find an equation of a line that is perpendicular to the line $x = 4$ that contains the point $(4, - 5)$ . Write the equation in slope-intercept form.

Short Answer

Expert verified

The equation of the line that is perpendicular to the line $x = 4$ is $y = 0 x - 5$ .

Step by step solution

Step 1. Given data

The given equation of the line is $x = 4$

The point through which the line passes $(4, - 5)$

Step 2. Equation of the perpendicular line

To find the equation we have the point-slope formula, that is $y - y_{1} = m (x - x_{1})$

Here we have to find the slope to use this formula.

So as we know the new line will be perpendicular to $x = 4$ . Since this line is vertical, its perpendicular will be horizontal. Therefore the slope, $m = 0$

Therefore, substituting the given point and slope in the point-slope formula we get,

$y - (- 5) = 0 (x - 4) y + 5 = 0 y = - 5$

Thus the equation of the perpendicular line is $y = - 5$

The slope-intercept formula is $y = m x + b$

Therefore, the equation in the slope-intercept form is $y = 0 x - 5$

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Find an equation of a line that is perpendicular to the line $x = 4$ that contains the point $(4, - 5)$ . Write the equation in slope-intercept form.

Short Answer

Step by step solution

Step 1. Given data

Step 2. Equation of the perpendicular line

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Find an equation of a line that is perpendicular to the line x=4that contains the point (4,−5). Write the equation in slope-intercept form.

Short Answer

Step by step solution

Step 1. Given data

Step 2. Equation of the perpendicular line

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Applied Mathematics

Logic and Functions

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find an equation of a line that is perpendicular to the line $x = 4$ that contains the point $(4, - 5)$ . Write the equation in slope-intercept form.