Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 2 - Functions, Equations, and Graphs - 2-3 Linear Functions and Slope-Intercept Form - Practice and Problem-Solving Exercises - Page 79: 47


slope = 0 y-intercept = 3

Work Step by Step

The slope of a line is always equal to the change in y divided by the change in x. Sometimes change can be represented by the Greek letter delta (which looks like a triangle), but it just means the difference between two points. The slope can be found by picking any two points on the line. I chose (0,3) and (3,3), but any others will work just as well. $x_{1}=0$ $y_{1}=3$ $x_{2}=3$ $y_{2}=3$ Simply divide the change in y (3-3) by the change in x (0-3): $m=\frac{y_{1}-y_{2}}{x_{1}-x_{2}}=\frac{3-3}{0-3}=0$. Since your numerator is 0, your slope is 0. Your y-intercept is the point where the line crosses the y-axis. This can be found by plugging x=0 into the line equation. However, since we are not given an equation, you can look at the graph and see that when x=0, y=3. So, the y-intercept =3.
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