Question

solve the problem
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 )
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.

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

compare functions

Explanation:

Step1: Find slope of the graph

Take two points on the red line, e.g., (-2, 0) and (0, 2). Slope $m = \frac{2-0}{0-(-2)} = 1$.

Step2: Compare slopes of options

• 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 to 1)
• E: $m=\frac{1}{2}=0.5$ (less than 1)

Only E has a slope less than 1.

Answer:

E. $y=\frac{1}{2}x + 5$