Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 78

Chapter 3, Problem 78

Give the slope and y-intercept of each line whose equation is given. Assume that B ≠ 0. Ax = By - C

Verified step by step guidance

Start with the given equation: \(Ax = By - C\).

Rearrange the equation to solve for \(y\) in terms of \(x\). Add \(C\) to both sides and then divide both sides by \(B\): \(By = Ax + C \implies y = \frac{A}{B}x + \frac{C}{B}\).

Identify the slope \(m\) from the equation in slope-intercept form \(y = mx + b\). Here, the slope is \(m = \frac{A}{B}\).

Identify the y-intercept \(b\) from the equation. The y-intercept is the constant term \(b = \frac{C}{B}\).

Summarize: The slope of the line is \(\frac{A}{B}\) and the y-intercept is \(\frac{C}{B}\).

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Key Concepts

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

Slope-Intercept Form of a Line

The slope-intercept form of a line is y = mx + b, where m represents the slope and b represents the y-intercept. Converting a given equation into this form helps identify these values directly.

Rearranging Linear Equations

To find the slope and y-intercept from an equation like Ax = By - C, you must isolate y on one side. This involves algebraic manipulation such as adding, subtracting, and dividing terms to rewrite the equation in slope-intercept form.

Slope and Y-Intercept Definitions

The slope measures the steepness of a line, calculated as the ratio of vertical change to horizontal change. The y-intercept is the point where the line crosses the y-axis, found by setting x = 0 in the equation.

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Slope-Intercept Form

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