Question

b. you have $75 to spend. how many competitions can you attend?
you can attend \square competitions.

Explanation:

Step1: Find the linear equation

First, identify two points on the line: $(0, 50)$ and $(10, 140)$. Calculate the slope $m$:
$m = \frac{140 - 50}{10 - 0} = \frac{90}{10} = 9$
The y-intercept $b$ is 50, so the equation is $y = 9x + 50$, where $y$ is total cost, $x$ is number of competitions.

Step2: Substitute $y=75$ and solve for $x$

Set $75 = 9x + 50$, then rearrange to solve for $x$:
$9x = 75 - 50$
$9x = 25$
$x = \frac{25}{9} \approx 2.78$
Since we can't attend a fraction of a competition, we take the whole number part.

Answer:

2