Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 1 - Graphs - 1.3 Lines - 1.3 Assess Your Understanding - Page 31: 91

Answer

The slope is $\frac{3}{2}$. The $y$-intercept is $0$. Refer to the graph below.

Work Step by Step

The slope of the line can be obtained by looking at the coefficient of $x$ in the slope-intercept form. Isolate $y$ to obtain: $2y-3x=0$ $2y=3x$ $y=\frac{3}{2}x$ Thus, the slope is $\frac{3}{2}$. By definition, the $y$-intercept is the constant in the slope-intercept form of the equation. For $y=\frac{3}{2}x$, the constant is $0$, therefore the $y$-intercept is $0$. Plot the point $(0, 0)$. Then using the slope, which is $\frac{3}{2}$, move $2$ units to the right and $3$ units up to reach $(2, 3)$. Connect the two points using a straight line to complete the graph. Refer to the graph above.
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