Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter F - Foundations: A Prelude to Functions - Section F.3 Lines - F.3 Assess Your Understanding - Page 30: 54



Work Step by Step

The equation of a line in the point-slope form is the following: $y-y_1=m(x-x_1)$, where $m$ is the slope and the point $(x_1,y_1)$ is on the graph. Here, our line's slope can be calculated by the formula: $m=\frac{y_2-y_1}{x_2-x_1}$, where the points $(x_1,y_1)$ and $(x_2,y_2)$ are on the line. In this exercise, we are given the two intercepts, which means that the points $(-4,0)$ (from the x-intercept) and $(0,4)$ (from the y-intercept) are on the line. We can plug in the given two points to calculate the slope: $m=\frac{4-0}{0-(-4)}=\frac{4}{4}=1$ Now we can just take one of the given points and complete the equation. Therefore the equation can be written as: $y-0=1(x-(-4))$ $y=x+4$
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