Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 3 - Parallel and Perpendicular Lines - 3-7 Equations of Lines in the Coordinate Plane - Practice and Problem-Solving Exercises - Page 195: 56


$y = -2x + 4$

Work Step by Step

We know that the x-intercept is the point on a line where it crosses the x-axis; it is also the value of $x$ when $y = 0$. For this line, the x-intercept is $2$. The y-intercept is the point on a line where it crosses the y-axis; it is also the value of $y$ when $x = 0$. For this line, the y-intercept is $4$. Given this information, we already have two points on our line: the x-intercept coordinate $(2, 0)$ and the y-intercept coordinate$(0, 4)$. We can use these two points to find the slope of the line first. Let's use the formula to find the slope $m$ given two points: $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line. Let's plug in these values into this formula: $m = \frac{4 - 0}{0 - 2}$ Subtract the numerator and denominator to simplify: $m = \frac{4}{-2}$ Divide the numerator and denominator by their greatest common denominator, which is $2$: $m = -2$ Now that we have the slope, we can use one of the points and plug these values into the point-slope equation, which is given by the formula: $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point on the line. Let's plug in the points and slope into the formula: $y - 0 = -2(x - 2)$ We can get rid of the $0$: $y = -2(x - 2)$ Use the distributive property on the right side of the equation to rewrite this equation in slope-intercept form: $y = -2x + 4$ This equation is now in slope-intercept form.
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