Question

identifying a system of equations
anna wants to take fitness classes. she compares two gyms to determine which would be the best deal for her. fit fast charges a set fee per class. stepping up charges a monthly fee, plus an additional fee per class. what is the system of equations representing these costs?
○ $y = 5.5x$ and $y = 7.5x + 10$
○ $y = 7.5x$ and $y = 5.5x$
○ $y = 7.5x$ and $y = 5.5x + 10$
○ $y = 7.5x + 10$ and $y = 5.5x + 10$

Explanation:

Step1: Find Fit Fast's equation

Fit Fast has no monthly fee, so it's a proportional relationship. Use point $(2,16)$:
Slope $m = \frac{16}{2} = 8$? No, wait use $(4,32)$: $m = \frac{32}{4}=8$? No, match options: wait, check $(2,16)$: $y=8x$ not an option, wait check the upper line: starts at $(0,10)$, so y-intercept $b=10$. Use point $(4,32)$: $32 = 4m +10$, so $4m=22$, $m=5.5$. That's Stepping Up (monthly fee + per class). Fit Fast: passes through $(0,0)$, use $(4,32)$: $32=4m$, $m=8$? No, wait $(2,16)$: $16=2m$, $m=8$. Wait no, options have 7.5 and 5.5. Wait, check $(4,32)$ for $y=7.5x$: $7.5*4=30$, no. $y=8x$ is 32. Wait, maybe the orange line is $(2,15)$? Oh, misread: orange point is $(2,15)$. So Fit Fast: $(2,15)$, slope $m=\frac{15}{2}=7.5$, so $y=7.5x$.

Step2: Find Stepping Up's equation

Stepping Up has y-intercept $b=10$ (starts at $(0,10)$). Use point $(4,32)$:
$32 = 4m +10$
$4m = 32-10=22$
$m=\frac{22}{4}=5.5$
So equation: $y=5.5x +10$

Answer:

$y = 7.5x$ and $y = 5.5x + 10$