Question

at a country fair, a family pays a fixed entrance fee. they then purchase ride tickets, which each have the same cost. the table shows the relationship between the number of ride tickets, x, that are purchased and the total amount paid y, in dollars, for both the entrance fee and the ride tickets. which equation represents the relationship between x and y? a y = 3/2x + 35 b y = 3/2x - 65 c y = 3/2x + 101/3 d y = 3/2x + 71/3

Explanation:

Step1: Find the cost per ride ticket

The cost per ride ticket (slope) $m$ can be found using the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(10,50)$ and $(x_2,y_2)=(15,57.5)$. Then $m=\frac{57.5 - 50}{15 - 10}=\frac{7.5}{5}=1.5=\frac{3}{2}$.

Step2: Find the fixed - entrance fee (y - intercept)

We use the point - slope form $y=mx + b$ and substitute $m = \frac{3}{2}$, $x = 10$ and $y = 50$. So $50=\frac{3}{2}\times10 + b$. Simplify the right - hand side: $\frac{3}{2}\times10=15$, then $50 = 15 + b$. Solve for $b$: $b=50 - 15=35$.

Step3: Write the equation

The equation of the line is $y=\frac{3}{2}x+35$.

Answer:

A. $y=\frac{3}{2}x + 35$