Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 39

Chapter 3, Problem 39

Find the slope and y-intercept of each line, and graph it. 4y = -3x

Verified step by step guidance

Rewrite the given equation in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Start by isolating $y$ on one side of the equation: $4y = -3x$.

Divide both sides of the equation by 4 to solve for $y$: $y = \frac{-3x}{4}$.

Identify the slope $m$ and the y-intercept $b$ from the equation $y = -\frac{3}{4}x + 0$. Here, the slope $m$ is $-\frac{3}{4}$ and the y-intercept $b$ is 0.

Interpret the y-intercept: since $b = 0$, the line crosses the y-axis at the origin $(0,0)$.

To graph the line, plot the y-intercept at $(0,0)$, then use the slope $-\frac{3}{4}$ to find another point by moving down 3 units and right 4 units from the y-intercept, and draw the line through these points.

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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 an equation into this form makes it easier to identify these values directly and to graph the line.

Slope of a Line

The slope measures the steepness and direction of a line, calculated as the ratio of the change in y to the change in x (rise over run). A positive slope rises to the right, while a negative slope falls to the right.

Y-Intercept

The y-intercept is the point where the line crosses the y-axis, occurring when x = 0. It is represented by the constant term b in the slope-intercept form and is essential for graphing the line accurately.

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