Question

Write an equation of the line perpendicular to the graph of the line $8 x-y=10$ and containing the point (-1,1)

Name: Problem 67, Chapter 2: Precalculus: A Right Triangle Approach
Uploaded: 2020-07-31T19:52:13-08:00
Duration: 2 min 30 s
Channel: Ankit Gupta
Description: Write an equation of the line perpendicular to the graph of the line 8 x-y=10 and containing the point (-1,1)

   Write an equation of the line perpendicular to the graph of the line $8 x-y=10$ and containing the point (-1,1)

Precalculus: A Right Triangle Approach

Judith A. Beecher,… 4th Edition

Chapter 2, Problem 67

Instant Answer

Solved by Expert Ankit Gupta

07/31/2020

Step 1

The equation of the line is $8x - y = 10$. To find the slope, rewrite this equation in slope-intercept form $y = mx + b$, where $m$ is the slope. Show more…

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Write an equation of the line perpendicular to the graph of the line $8 x-y=10$ and containing the point (-1,1)

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Key Concepts

Slope-Intercept Form

This is a common way to express the equation of a line in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept. Converting an equation to this form makes it easier to identify the slope, which is crucial for determining relationships between lines, such as parallelism or perpendicularity.

Perpendicular Lines

Lines that are perpendicular to each other intersect at a right angle (90 degrees). The slopes of two perpendicular lines have a special relationship: they are negative reciprocals of each other. This means if one line has a slope m, the line perpendicular to it will have a slope of -1/m.

Point-Slope Form

This form of the equation of a line is used when you know a point on the line and its slope. It is expressed as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. It is particularly useful for writing the equation of a line when these two pieces of information are known.

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