## Thomas' Calculus 13th Edition

Published by Pearson

# Appendices - Section A.3 - Lines, Circles, and Parabolas - Exercises A.3 - Page AP-17: 13

#### Answer

$y=4x+4$

#### Work Step by Step

The line contains points $(x_{1},y_{1})=(0,4),\quad$(the y-intercept) $(x_{2},y_{2})=(-1,0),\quad$(the x-intercept) We calculate the increments, $\left\{\begin{array}{l} \Delta x=x_{2}-x_{1}=-1-0=-1\\ \Delta y=y_{2}-y_{1}=0-4=-4 \end{array}\right.$ Since $\Delta x\neq 0$, the slope is defined, $\displaystyle \qquad m=\frac{\Delta y}{\Delta x}=\frac{-4}{-1}=4$ The slope-intercept form a line equation is $y=mx+b,$ where $m$ = slope and $b$ = y-intercept. Here, $m=4$ and $b=4$ $y=4x+4$

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