College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 2 - Section 2.3 - Lines - 2.3 Assess Your Understanding: 56

Answer

$\color{blue}{y=x+4}$

Work Step by Step

RECALL: (1) The slope-intercept form of a line's equation is: $y=mx+b$ where $m$=slope and $b$ = y-intercept. (2) The x-intercept of a line is the point where $y=0$ and whose coordinates are $(x, 0)$. The given line has: y-intercept = $4$ x-intercept = $-4$ Substituting the y-intercept of $4$ to $b$ in the slope-intercept form above gives the tentative equation of the line: $y=mx+4$ The x-intercept is $-4$. This means that the point $(-4, 0)$ is on the graph of the line. To find the value of $m$, substitute $0$ to $y$ and $-4$ to $x$ into the tentative equation above to obtain: $y=mx+4 \\0=m(-4)+4 \\0=-4m+4 \\0+4m=4 \\4m=4 \\m=\frac{4}{4} \\m=1$ Thus, the equation of the line is: $y=1(x) + 4 \\\color{blue}{y=x+4}$
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