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 - Page 178: 41



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 slope of a line can be solved using the formula $m=\dfrac{y_2-y_1}{x_2-x_1}$ where $(x_1, y_1)$ and $(x_2, y_2)$ are points on the line. The given line contains the points $(-1, 3)$ and $(1, 1)$. Solve for the slope using the formula in $(2)$ above to obtain: $m=\dfrac{3-1}{-1-1} \\m=\dfrac{2}{-2} \\m=-1$ Thus, the tentative equation of the line is: $y=-1(x)+b \\y=-x+b$ To find the value of $b$, substitute the x and y values of the point $(1, 1)$ into the tentative equation above to obtain: $y=-x+b \\1=-1+b \\1+1=b \\2=b$ Using the y-intercept, we find that the equation of the line is: $\color{blue}{y=-x+2}$
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