the graph represents the cost of a subscription to a newspaper. what is the constant of variation for the…

the graph represents the cost of a subscription to a newspaper. what is the constant of variation for the subscription cost based on the number of weeks? weekly newspaper subscription total cost ($) duration (weeks) $1.50 $7.50 $15.00 $30.00 (12, 90) (8, 60) (4, 30)

the graph represents the cost of a subscription to a newspaper. what is the constant of variation for the subscription cost based on the number of weeks? weekly newspaper subscription total cost ($) duration (weeks) $1.50 $7.50 $15.00 $30.00 (12, 90) (8, 60) (4, 30)

Answer

Explanation:

Step1: Identify the relationship and constant of variation.

The graph shows a linear relationship between Total Cost ($y$) and Duration ($x$) passing through the origin, representing a direct variation $y = kx$. The constant of variation, $k$, is the ratio $\frac{y}{x}$.

Step2: Choose a point from the graph.

Select any point on the line, for example, $(4, 30)$. Here, $x = 4$ weeks and $y = $30$.

Step3: Calculate the constant of variation.

Substitute the values of $x$ and $y$ into the formula $k = \frac{y}{x}$. $$k = \frac{30}{4}$$

Step4: Simplify the expression.

Calculate the value of the fraction. $$k = 7.5$$ The constant of variation is $7.50.

Answer:

$7.50