College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.3 - Lines - 1.3 Exercises: 30

Answer

$y=x-1$

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 slope of a line can be found 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. Solve for the slope to obtain: $m=\dfrac{3-(-2)}{4-(-1)} \\m=\dfrac{3+2}{4+1} \\m=\dfrac{5}{5} \\m=1$ Thus, the tentative equation of the line is: $y=1(x)+b \\y=x+b$ To find the value of $b$, substitute the coordinates of $(4, 3)$ into the tentative equation above to obtain: $y=x+b \\3 = 4+ b \\3-4 = b \\-1=b$ Therefore, the equation of the line is: $y=x+(-1) \\y=x-1$
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