Ch. 2 - Graphs and Functions

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

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 37

Chapter 3, Problem 37

Find the slope and y-intercept of each line, and graph it. 4x-y =7

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 with the equation: $4x - y = 7$.

Isolate $y$ on one side by subtracting \$4x$ from both sides: $-y = -4x + 7$.

Multiply both sides of the equation by $-1$ to solve for $y$: $y = 4x - 7$.

Identify the slope $m$ and the y-intercept $b$ from the equation $y = 4x - 7$. The slope is the coefficient of $x$, and the y-intercept is the constant term.

To graph the line, plot the y-intercept point $(0, b)$ on the coordinate plane, then use the slope $m$ to find another point by rising and running 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 is y = mx + b, where m represents the slope and b the y-intercept. Converting the given equation into this form helps identify these values directly, making it easier to analyze and 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). It indicates how much y changes for a unit change in x and is essential for understanding the line's behavior.

Y-Intercept of a Line

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

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Graphing Lines in Slope-Intercept Form

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