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Linear Regression and Correlation: Slope and Y-Intercept of a Linear Equation

Module by: Susan Dean, Dr. Barbara Illowsky

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.
Subfigure 1.1: If b > 0b > 0, the line slopes upward to the right. Subfigure 1.2: If b = 0b = 0, the line is horizontal. Subfigure 1.3: 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 1

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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