Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 1, Equations and Inequalities - 1.5 Use Problem Solving Strategies and Models - 1.5 Exercises - Skill Practice - Page 37: 11



Work Step by Step

The first step is to check how the numbers are progressing. Do the values progress through addition, subtraction, multiplication, or division? The equation is going to be in the format $y=mx+b$, and since the first $x$-value of $0$ corresponds to a $y$-value of $11$, if you substitute in the known values of $y$, $x$, and $b$, we would get $11=0m+b$. Because of the Zero Product Property, the product of $0$ and any other number is $0$, so the above equation results in $b=11$. Therefore, we can amend the general formula for the equation ($y=mx+b$, as mentioned above) to say $y=mx+11$. Now we can use another pair of $x$ and $y$ values to find the value of $m$. If we use the second pair, $15=1m+11$ $1m=m$, so $15=m+11$ $m=4$. Plugging in the known values of $m$ and $b$, the equation to represent this table is $y=4x+11$. It's probably a good idea to see if this equation applies to other $x$-and-$y$-value pairs, just to make sure. The third pair, for example, is 2 and 19. $19=(4\times2)+11=8+11=19$ $19=19$ Because the above statement works out to be true, the equation $y=4x+11$ does, in fact, apply to this question.
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