Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter F - Foundations: A Prelude to Functions - Section F.3 Lines - F.3 Assess Your Understanding - Page 31: 71


The slope is $2$. The $y$-intercept is $3$. See the graph below.

Work Step by Step

This form of the equation is the slope-intercept form. $y=mx+b$ In this form, the slope of the line equals to the coefficient of $x$ (which is $m$) and the $y$-intercept equals to the constant $b$. Therefore in the equation $y=2x+3$: The slope is $m=2$. The $y$-intercept is $3$. In order to graph the line, we have to sketch the $y$-intercept, that is $(0,3)$. As the slope equals to $2$, we can find another point that we can also sketch. The slope is the change in $y$ for every $1$ unit change of $x$. Thus, a slope of $2$ means a $1$-unit increase in $x$ will result to a $2$-unit increase in $y$. Using $(0,3)$ as the starting point and a slope of $2$, the coodinates of another point on the line would be: $(0+1,3+2)=(1,5)$ Plot the two points then connect them using a straigiht line. Refer to the graph above,
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