Precalculus (6th Edition)

Published by Pearson

Chapter 2 - Graphs and Functions - 2.5 Equations of Lines and Linear Models - 2.5 Exercises - Page 243: 43

Answer

slope = $\frac{3}{2}$ y-intercept: $(0, 1)$ Refer to the graph below.

Work Step by Step

Solve for $y$: $y-\frac{3}{2}x-1=0 \\y-\frac{3}{2}x-1+1=0+1 \\y-\frac{3}{2}x=1 \\y-\frac{3}{2}x+\frac{3}{2}x=1+\frac{3}{2}x \\y=\frac{3}{2}x+1$ This means that the given equation is equivalent to $y=\frac{3}{2}x+1$. RECALL: The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $(0, b)$ is the line's y-intercept. Thus, the equation $y=\frac{3}{2}x+1$ has a slope of $\frac{3}{2}$ and a y-intercept of $(0, 1)$. To graph the equation, perform the following steps: (1) Plot the y-intercept $(0, 1)$. (2) Use the slope to plot a second point. Since the slope is $\frac{3}{2}$, from $(0, 1)$, move 3 units up (the rise) and 2 units to the right (the run) to reach the point $(2, 4)$. Plot $(2. 4)$. (3) Connect the points using a straight line. (Refer to the graph in the answer part above)

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