A linear equation can be written as:
[tex]y=mx+b[/tex]
Let:
y = c = Cost
x = h = Hours
Using the data, we can create a 2x2 system of equations. So:
[tex]\begin{gathered} x=2,y=20 \\ 20=2m+b_{\text{ }}(1) \\ ---------- \\ x=8,y=50 \\ 50=8m+b_{\text{ }}(2) \end{gathered}[/tex]
Using elimination method:
[tex]\begin{gathered} (2)-(1) \\ 50-20=8m-2m+b-b \\ 30=6m \\ m=\frac{30}{6} \\ m=5 \\ so\colon \\ 20=2(5)+b \\ b=10 \end{gathered}[/tex]
Therefore,the linear equation is given by:
[tex]y=5x+10[/tex]
For a equation of the form y = mx + b
m = Slope (rate)
b = y-intercept (Initial value)
Therefore the hourly rate for renting a bicycle is $5 and the deposit is $10
