Question

solve the problems.
1 the graph shows a function.

which equation represents a function with a rate of change that is less than the rate of change of the function shown in the graph? select all that apply.
a $y=2x-4$
b $y=\frac{5}{3}x + 1$
c $y=\frac{3}{2}x - 1$
d $y=x + 3$
e $y=\frac{x}{2} + 5$
2 for each verbal description, write in the correct equation from the choices provided.
samantha begins her road trip with 30 gallons of gasoline in the tank of her van. her van gets 25 miles to the gallon. let $y$ represent the number of gallons of gasoline in the tank after $x$ miles of travel.
evan has a cell phone plan that costs $30 per month and $0.25 per minute of phone use. let $y$ represent the monthly cost of cell phone service after $x$ minutes of phone use.
$y = 30 + 0.25x$
$y = 30 - \frac{x}{25}$
$y = 25 - \frac{x}{30}$
$y = 25 + 0.30x$

Explanation:

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Problem 1

Step1: Find graph's slope

The graph has a y-intercept at $(0,2)$ and passes through $(3,5)$. Slope $m = \frac{5-2}{3-0} = 1$.

Step2: Compare slopes of options

We need slopes less than 1:

• A: $m=2$ (greater than 1)
• B: $m=\frac{5}{3}\approx1.67$ (greater than 1)
• C: $m=\frac{3}{2}=1.5$ (greater than 1)
• D: $m=1$ (equal, not less)
• E: $m=\frac{1}{2}=0.5$ (less than 1)

1. For Samantha's van: She starts with 30 gallons, and uses $\frac{1}{25}$ gallons per mile (since 25 miles use 1 gallon). So remaining gallons $y$ decrease by $\frac{x}{25}$ from 30.
2. For Evan's phone plan: He pays a fixed $30 plus $0.25 per minute, so total cost $y$ is 30 plus $0.25x$.

Answer:

E. $y=\frac{x}{2}+5$

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Problem 2