Question

the table shows the total cost spent at the state fair.
number of ride tickets purchased|total cost ($)
1|14.50
2|17.00
3|19.50
4|22.00
part a: write an equation to represent the relationship.
part b: what is the total cost if 13 ride tickets are purchased?

Explanation:

Step1: Find the slope

The slope $m$ of a linear - equation $y = mx + b$ can be found using the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $x$ be the number of ride - tickets purchased and $y$ be the total cost. Using the points $(1,14.50)$ and $(2,17.00)$, we have $m=\frac{17.00 - 14.50}{2 - 1}=\frac{2.50}{1}=2.50$.

Step2: Find the y - intercept

We know that $y=mx + b$. Substitute $m = 2.50$, $x = 1$, and $y = 14.50$ into the equation: $14.50=2.50\times1 + b$. Solving for $b$, we get $b=14.50−2.50 = 12$.

Step3: Write the equation

The equation representing the relationship is $y = 2.5x+12$.

Step4: Calculate the total cost for 13 tickets

Substitute $x = 13$ into the equation $y = 2.5x+12$. Then $y=2.5\times13 + 12$. First, calculate $2.5\times13=32.5$. Then $y=32.5+12=44.5$.

Answer:

Part A: $y = 2.5x + 12$
Part B: $44.5$