# Chapter 7 - Algebra: Graphs, Functions, and Linear Systems - 7.2 Linear Functions and Their Graphs - Exercise Set 7.2 - Page 430: 36

(a) $y=\dfrac{5}{4}x$ (b) slope = $\dfrac{5}{4}$, y-intercept = $0$ (c) Refer to the image below for the graph.

#### Work Step by Step

(a) The slope-intercept form is $y=mx+b$ where m = slope and b = y-intercept. Divide $4$ on both sides to obtain: $y=\dfrac{5}{4}x$ (b) The equation has $m=\frac{5}{4}$ and $b=0$. Thus, slope = $\dfrac{5}{4}$ y-intercept = $0$ (c) Plot the y-intercept point $(0,0)$. From $(0,0)$, move 5 units up (the rise) and 4 units to the right (the run). These steps lead to the point $(4,5)$. Connect the two points using a line to complete the graph.

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