Ch. 2 - Functions and Graphs

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

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 66a

Chapter 3, Problem 66a

In Exercises 59-66, a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. 4y+ 28 = 0

Verified step by step guidance

Rewrite the given equation in slope-intercept form (y = mx + b). Start by isolating the term with 'y' on one side of the equation. Subtract 28 from both sides to get 4y = -28.

Divide both sides of the equation by 4 to solve for 'y'. This simplifies to y = -7.

Identify the slope (m) and y-intercept (b) from the slope-intercept form y = mx + b. In this case, the slope (m) is 0 (since there is no x-term), and the y-intercept (b) is -7.

To graph the linear function, plot the y-intercept (0, -7) on the coordinate plane. Since the slope is 0, the line is horizontal, meaning it does not rise or fall as x changes.

Draw a horizontal line through the point (0, -7) to complete the graph of the linear function.

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Key Concepts

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

Slope-Intercept Form

The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope and b represents the y-intercept. This form is particularly useful for quickly identifying the slope and y-intercept of a line, which are essential for graphing linear functions.

Slope

The slope of a line measures its steepness and direction, calculated as the change in y over the change in x (rise over run). A positive slope indicates the line rises from left to right, while a negative slope indicates it falls. Understanding slope is crucial for interpreting the relationship between variables in a linear equation.

Y-Intercept

The y-intercept is the point where a line crosses the y-axis, represented by the value of y when x is zero. In the slope-intercept form, this value is denoted by b. Identifying the y-intercept is important for graphing linear equations, as it provides a starting point on the graph.

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