Question

a. Juan also has a gym membership. Juan paid $21 for 4 visits and $41 for 9 visits. what is the y intercept and slope. b. Last month Juan visited the gym 29 times what was the cost he had to pay last month?

Answer 1

Let's begin by identifying key information given to us:

Juan paid $21 for 4 visits

Juan paid $41 for 9 visits

This is represented as:

`\begin{gathered} (x_1,y_1)=(4,21) \\ (x_2,y_2)=(9,41) \\ slope(m)=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1) \\ slope(m)=(41-21)/(9-4)=(20)/(5)=4 \\ slope(m)=4 \\ \\ \end{gathered}`

We will proceed to solve for the equation for the straight line using the point-slope form. We have:

`\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(4,21) \\ y-21=4(x-4) \\ y-21=4x-16 \\ \text{Add ''21'' to both sides, we have:} \\ y-21+21=4x-16+21 \\ y=4x+5 \\ \\ y-intercept\Rightarrow x=0 \\ when\colon x=0 \\ y=4(0)+5=0+5=5 \\ y=5 \\ \\ \therefore y-intercept(at,ZeroVisit)=\text{\$}5 \end{gathered}`

Last month Juan visited the gym 29 times. This implies that x = 29. We will find the cost of this by substituting the value of x into the equation of the line:

`\begin{gathered} y=4x+5 \\ x=29 \\ \Rightarrow y=4(29)+5=116+5=121 \\ y=\text{\$}121 \end{gathered}`