Question

marcus is organizing a school dance and is considering buying tickets to a local amusement park for his class to enjoy. the table shows the total cost marcus will pay based on the number of tickets he purchases. part a: which equation represents the relationship between y, the cost of x tickets? a. y = 6x + 6 b. y = 7x + 5 c. y = 8x + 4 d. y = 7x + 6 part b: how much will marcus pay if he purchases 9 tickets? a. $68 b. $72 c. $69 d. $75

Explanation:

Step1: Find the slope and y - intercept

We know the equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Let's take two points from the table, say $(1,12)$ and $(2,19)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{19 - 12}{2 - 1}=7$. Substitute $x = 1$, $y = 12$ and $m = 7$ into $y=mx + b$, we get $12=7\times1 + b$, then $b=12 - 7=5$. So the equation is $y = 7x+5$.

Step2: Calculate cost for 9 tickets

For part B, we use the equation $y = 7x+5$. Substitute $x = 9$ into the equation, $y=7\times9 + 5=63 + 5=68$.

Answer:

Part A: B. $y = 7x + 5$
Part B: A. $\$68$