Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 5 - Linear Functions - 5-5 Standard Form - Practice and Problem-Solving Exercises - Page 327: 57


The x-intercept is $4$. The y-intercept is $\frac{-8}{5}$

Work Step by Step

To find the x-intercept and y-intercept of the line, we first need to find the equation of the line. We can use the two points given to formulate the point-slope form. Let's first find the slope: $m=\frac{y_2-y_1}{x_2-x_1}$, where $m$ is the slope and $(x_1,y_1)$ and $(x_2,y_2)$ are points on the line. Let's plug in our two points into this formula: $m=\frac{-2-0.4}{-1-5}=\frac{2}{5}$ Since we have the slope and two points, we can use the point-slope form, which is given by the following formula: $y-y_1=m(x-x_1)$ Let's plug in the slope and a point into this formula: $y-(-2)=\frac{2}{5}(x-(-1))$ $y+2=\frac{2}{5}(x+1)$ This is the point-slope formula of the equation. To find the x-intercept, we set y equal to 0: $0+2=\frac{2}{5}(x+1)$ Use the distributive property on the right side of the equation: $\frac{2}{5}x+\frac{2}{5}=2$ $x=4$ To find the y-intercept, we set x equal to 0: $y+2=\frac{2}{5}(0+1)$ $y+2=\frac{2}{5}$ $y=\frac{-8}{5}$ The x-intercept is $4$. The y-intercept is $\frac{-8}{5}$.
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