Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 1 - Linear Functions - 1.1 Slopes and Equations of Lines - 1.1 Exercises - Page 13: 21


$y=6x -3.5$.

Work Step by Step

RECALL: (i) The slope-intercept form of a line's equation is $y=mx+b$ where $m$ = slope and $b$ = y-intercept. (ii) The formula for slope is $m=\dfrac{y_2-y_1}{x_2-x_1}$. Solve for the slope using the formula above to have: $m=\dfrac{-2-\frac{1}{2}}{\frac{1}{4}-\frac{2}{3}}=\dfrac{-\frac{5}{2}}{-\frac{5}{12}}=\dfrac{-5}{2} \cdot \dfrac{-12}{5}=6$ Thus, the tentative equation of the line is $y=6x + b$. Solve for the value of $b$ by substituting the x and y-coordinates of one point into the tentative equation to have: $y=6x+b \\-2 = 6(\frac{1}{4})+b \\-2=1.5+b \\-2-1.5=b \\-3.5=b$ Therefore, the equation of the line in slope-intercept form is $y=6x -3.5$.
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