## Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 4 - An Introduction to Functions - 4-2 Patterns and Linear Functions - Practice and Problem-Solving Exercises - Page 244: 13

#### Answer

The table represents a linear function. The graph is attached below. The equation for the relationship is y=11.2-$\frac{1}{17}$x The relationship exhibited is that the initial gallons of gas is 11.2 before any miles are travelled and that for every 17 miles travelled which is independent, 1 gallon of gas i.e. the dependent variable is used and so slope is -$\frac{1}{17}$

#### Work Step by Step

a. The relationship is linear as it passes the vertical line test. b. The equation for the relationship is y=11.2-$\frac{1}{17}$x The slope was calculated by using (0,11.2) (17,10.2). m=$\frac{y2-y1}{x2-x1}$ = $\frac{10.2-11.2}{17-0}$ = - $\frac{1}{17}$ The y-int is 11.2 because this occurs when the independent variable is equal to 0.

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