Ch. 2 - Functions and Graphs

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

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 46

Chapter 3, Problem 46

In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line. y = (2/5)x - 1

Verified step by step guidance

Step 1: Recognize that the given equation is in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.

Step 2: Identify the slope (m) from the equation y = (2/5)x - 1. Here, m = 2/5. This means the line rises 2 units for every 5 units it moves to the right.

Step 3: Identify the y-intercept (b) from the equation y = (2/5)x - 1. Here, b = -1. This means the line crosses the y-axis at the point (0, -1).

Step 4: To graph the line, start by plotting the y-intercept (0, -1) on the coordinate plane. This is the starting point of the line.

Step 5: Use the slope (2/5) to find another point on the line. From (0, -1), move up 2 units and to the right 5 units to locate the next point. Draw a straight line through these points to complete the graph.

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Key Concepts

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

Slope

The slope of a line measures its steepness and direction, represented as 'm' in the slope-intercept form of a linear equation, y = mx + b. It indicates how much y changes for a unit change in x. In the equation y = (2/5)x - 1, the slope is 2/5, meaning for every 5 units you move to the right on the x-axis, the line rises by 2 units.

Y-Intercept

The y-intercept is the point where the line crosses the y-axis, represented as 'b' in the slope-intercept form y = mx + b. It indicates the value of y when x is zero. In the equation y = (2/5)x - 1, the y-intercept is -1, meaning the line crosses the y-axis at the point (0, -1).

Graphing Linear Equations

Graphing a linear equation involves plotting points that satisfy the equation and drawing a straight line through them. To graph y = (2/5)x - 1, start at the y-intercept (0, -1) and use the slope (2/5) to find another point. From (0, -1), move up 2 units and right 5 units to reach (5, 1), then draw the line through these points.

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