Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 4 - Cumulative Review - Page 333: 25

Answer

$$x-5y=-23$$

Work Step by Step

Recall the formula for slope: $$slope(m)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}, x2 - x1\ne0$$ Given the points $(2, 5)$ and $(-3, 4)$, we can find the slope: $$slope(m)=\frac{4-5}{-3-2}$$ $$slope(m)=\frac{-1}{-5}$$ $$slope(m)=\frac{1}{5}$$ Recall the slope-intercept form: $y=mx+b$ Use either of the points and the computed value of the slope to find the intercept, $b$. $Point\:1 (2,5)$ $m=\frac{1}{5}$ $$y=mx+b$$ $$5=(\frac{1}{5})(2)+b$$ $$5=\frac{2}{5}+b$$ Subtract $\frac{2}{5}$ from both sides: $$5-\frac{2}{5}=\frac{2}{5}-\frac{2}{5}+b$$ $$\frac{25}{5}-\frac{2}{5}=b$$ $$\frac{23}{5}=b$$ Thus, we have the equation $y=\frac{1}{5}x+\frac{23}{5}$. Rewriting this in the form $Ax + By = C$: $$-\frac{23}{5}=\frac{1}{5}x-y$$ $$\frac{1}{5}x-y=-\frac{23}{5}$$ Multiply the whole equation by $5$: $$[\frac{1}{5}x-y=-\frac{23}{5}]\cdot5$$ $$x-5y=-23$$
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