Explain/show why the table below represents a proportional relationship

The table not represent a proportional relationship

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

we have

For x=3, y=17

Find the value of k

----->

For x=5, y=27

Find the value of k

----->

For x=8, y=42

Find the value of k

----->

For x=9, y=47

Find the value of k

----->

The values of k are different

therefore

The table not represent a proportional relationship

Find the slope of the line

(3,17) and (9,47)

m=(47-17)/(9-3)=30/6=5

Find the equation of the line with m=5 and point (3,17)

y-y1=m(x-x1)

substitute

y-17=5(x-3)

y=5x-15+17

y=5x+2

This is the linear equation that represent the points in the table, but this equation not represent a proportional relationship (The line not passes through the origin)

4a. is 3 miles every hour

4b. is 1/3 of an hour per mile

step-by-step explanation: