Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

2. Graphs of Equations

Lines

College Algebra

2. Graphs of Equations

Lines

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1:48 minutes

Problem 49

Textbook Question

Find the slope of the line satisfying the given conditions. See Example 5. vertical, through (4, -7)

Verified step by step guidance

A vertical line has an undefined slope.

Vertical lines are parallel to the y-axis.

The equation of a vertical line is of the form x = a, where a is the x-coordinate of any point on the line.

Since the line passes through the point (4, -7), the equation of the line is x = 4.

Therefore, the slope of the line is undefined.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Slope of a Line

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a linear equation, y = mx + b. It is calculated as the ratio of the change in the y-coordinates to the change in the x-coordinates between two points on the line. A positive slope indicates the line rises as it moves from left to right, while a negative slope indicates it falls.

Vertical Lines

A vertical line is a line that goes straight up and down, having an undefined slope. This occurs because the change in x-coordinates is zero, leading to a division by zero when calculating slope. Vertical lines are represented by equations of the form x = a, where 'a' is a constant, indicating that all points on the line have the same x-coordinate.

Point-Slope Form

The point-slope form of a linear equation is used to express the equation of a line given a point on the line and its slope. It is written as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. This form is particularly useful for quickly writing the equation of a line when the slope and a point are known.