Question

the graph shows the relationship between the time katrina spends jogging and her total distance traveled. which function represents the relationship?
options:
( y = \frac{1}{3}x )
( y = \frac{1}{6}x )
( y = 3x )
( y = 6x )

Explanation:

Step1: Identify a point on the line

Choose the point $(1, 3)$ (from the graph: at time $x=1$, distance $y=3$).

Step2: Test the point in each function

• For $y=\frac{1}{3}x$: $\frac{1}{3}(1)=\frac{1}{3}

eq 3$

• For $y=\frac{1}{6}x$: $\frac{1}{6}(1)=\frac{1}{6}

eq 3$

• For $y=3x$: $3(1)=3$, which matches.
• For $y=6x$: $6(1)=6

eq 3$

Step3: Verify with another point

Use $(2, 6)$: $y=3(2)=6$, which matches the graph.

Answer:

C. $y=3x$