Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 4 - Writing Linear Functions - 4.1-4.3 - Quiz - Page 194: 7

Answer

The linear function is $f(x)=-x+2$.

Work Step by Step

Rewrite as shown below. $f(0)=2$ as $(0,2)$ and $f(5)=-3$ as $(5,-3)$ Let $(x_1,y_1)=(0,2)$ and $(x_2,y_2)=(5,-3)$. Slope $\Rightarrow m =\frac{y_2-y_1}{x_2-x_1}$ Substitute all the values. $\Rightarrow m =\frac{-3-2}{5-0}$ Simplify. $\Rightarrow m =\frac{-5}{5}$ $\Rightarrow m =-1$ The point-slope form. $\Rightarrow y-y_1=m(x-x_1)$ Substitute all the values. $\Rightarrow y-(2)=-1(x-0)$ Simplify. $\Rightarrow y-2=-x$ Add $2$ to each side. $\Rightarrow y-2+2=-x+2$ Simplify. $\Rightarrow y=-x+2$ Hence, the linear function is $f(x)=-x+2$.
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