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 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.
van has a cell phone plan that costs $30 per month and $0.25 per minute of phone use. let represent the monthly cost of cell phone ice after x minutes of phone use.

Explanation:

Step1: Find slope of graph

The graph passes through (0,3) and (-3,0). Slope $m=\frac{0-3}{-3-0}=1$.

Step2: Compare slopes of options

A: 2; B: $\frac{5}{3}\approx1.67$; C: $\frac{3}{2}=1.5$; D:1; E: $\frac{1}{2}=0.5$. Need slopes <1.

Step1: Gasoline equation logic

Initial gas:30 gallons. Gas used per mile: $\frac{1}{25}$ gallons. So $y=30-\frac{x}{25}$.

Step2: Cell phone equation logic

Fixed cost:30. Cost per minute:0.25. So $y=30+0.25x$.

Answer:

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