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: 55


The x-intercept is $6$. The y-intercept is $6$.

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: $m = \frac{2 - 8}{4 - (-2)}$ Simplify by adding or subtracting in the numerator and denominator: $m = \frac{-6}{6}$ Divide both the numerator and denominator by their greatest common factor, $6$: $m = -1$ 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: $y - 2 = -1(x - 4)$ Simplify the right side of the equation: $y - 2 = -x + 4$ This is the point-slope formula of the equation. To find the x-intercept, we set $y$ equal to $0$: $0 - 2 = -x + 4$ Add $2$ to both sides of the equation to move constants to one side of the equation: $0 = -x + 6$ Add $x$ to both sides of the equation: $x = 6$ To find the y-intercept, we set $x$ equal to $0$: $y - 2 = -0 + 4$ Add $2$ to each side of the equation: $y = 6$ The x-intercept is $6$. The y-intercept is $6$.
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