Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.10 - Lines - 1.10 Exercises - Page 115: 43



Work Step by Step

For the purposes of this question, we will be using slope-intercept form, or as your teacher has most likely demonstrated, y=mx+b. In slope intercept form, the constant "m" represents the slope, and the constant "b" represents the y-intercept, or where the line crosses the y-axis. Our first step will be to find "m" or the slope. We are given a line (x+2y=6), that is said to be parallel to the line we are looking for; this means the slopes are equal. If we use simple algebra to change the parallel line into slope-intercept form (subtract x and divide both sides by 2) we get y=$\frac{-x}{2}$+3. The slope of this equation is $\frac{-1}{2}$, so that will be the "m" of the equation we are trying to find. Next, we will find "b" or the y-intercept. We were given that the point (1,-6) exists on our line. We can use the information we currently have to then find the y intercept. We will plug in 1 for x, -6 for y, and $\frac{-1}{2}$ for m. We end up with -6=( $\frac{-1}{2}$)(1)+b. If we solve this algebraically (by adding $\frac{1}{2}$) we get b=-5.5 Finally, we have to put all this together. We have found that m= $\frac{-1}{2}$, and b=-5.5. So our final answer is y=$\frac{-x}{2}$-5.5
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