Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - Chapter 2 Test Prep - Review Exercises: 61

Answer

(a) slope-intercept form: $\color{blue}{y=-2x+1}$ (b) standard form: $\color{red}{2x+y=1}$

Work Step by Step

RECALL: (1) 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. (2) The standard form of a line's equation is $Ax+By=C$ where $A\ge0$ and A, B, and C are integers. (3) The point-slope form of a line's equation is $y-y_1=m(x-x_1)$ where $m$=slope and $(x_1, y_1)$ is a point on the line. The given line has a slope of $-2$ and contains the point $(3, -5)$. This means the point-slope form of the line's equation is: $$y-(-5)=-2(x-3) \\y+5=-2(x-3)$$ (a) slope-intercept form The slope-intercept form of the line can be derived from the equation above: $y+5=-2(x-3) \\y+5=-2(x)-(-2)(3) \\y+5=-2x+6 \\y+5-5=-2x+6-5 \\\color{blue}{y=-2x+1}$ (b) standard form The standard form of the line's equation can be derived from the slope-intercept form: $y=-2x+1 \\y+2x+=-2x+1+2x \\\color{red}{2x+y=1}$
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