Respuesta :
Answer:
This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
Step-by-step explanation:
Given
Time ------ 0 ----- 2 ------- 4 ----- 6 -----8.
Cost ------- 0 ----- 10 ----- 20 ----30 ----40
Required
Explain why or why not it is a direct variation?
First, we calculate the slope of the table.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where:
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (8,40)[/tex]
So:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{40 - 0}{8 - 0}[/tex]
[tex]m = \frac{40}{8}[/tex]
[tex]m = 5[/tex]
Next, we determine the equation using
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - 0 = 5(x - 0)[/tex]
[tex]y = 5(x)[/tex]
[tex]y = 5x[/tex]
The above shows a direct variation with 5 as its constant of proportionality of variation.