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Slope and Y-Intercept of a Linear Equation

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Summary: This module provides an overview of Linear Regression and Correlation: Slope and Y-Intercept of a Linear Equation as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

For the linear equation y = a + bx y=a+bx, bb = slope and aa = y-intercept.

From algebra recall that the slope is a number that describes the steepness of a line and the y-intercept is the y coordinate of the point (0,a)(0,a) where the line crosses the y-axis.

Figure 1: Three possible graphs of y = a + bx y=a+bx.
(a) If b > 0b > 0, the line slopes upward to the right. (b) If b = 0b = 0, the line is horizontal. (c) If b < 0b < 0, the line slopes downward to the right.
A straight line with a slope up and to the right.A flat line from left to right with no slope.A straight line with a slope down and to the right.

Example 1

Svetlana tutors to make extra money for college. For each tutoring session, she charges a one time fee of $25 plus $15 per hour of tutoring. A linear equation that expresses the total amount of money Svetlana earns for each session she tutors is y=25+15xy=25+15x.

Problem 1

What are the independent and dependent variables? What is the y-intercept and what is the slope? Interpret them using complete sentences.

Solution

The independent variable (x) is the number of hours Svetlana tutors each session. The dependent variable (y) is the amount, in dollars, Svetlana earns for each session.

The y-intercept is 25 (a = 25). At the start of the tutoring session, Svetlana charges a one-time fee of $25 (this is when x = 0). The slope is 15 (b = 15). For each session, Svetlana earns $15 for each hour she tutors.

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