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: 55

Answer

$\\\color{blue}{y=\dfrac{1}{2}x-1}$

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