Question

Write a linear equation, slope intercept form, to find the total cost of C for L lessons

Answer 1

The form of the linear equation is

`y=mx+b`

m is the slope

b is the y-intercept (initial value at x = 0)

Since the cost is C and the number of dances is L, then

The equation should be

`C=mL+b`

We will use the given information to find m and b

Since 7 lessons cost $82 dollars, then

Substitute C by 82 and L by 7

`\begin{gathered} 82=m(7)+b \\ 82=7m+b \\ 7m+b=82\rightarrow(1) \end{gathered}`

Since 11 lessons cost $122, then

Substitute C by 122 and L by 11

`\begin{gathered} 122=m(11)+b \\ 122=11m+b \\ 11m+b=122\rightarrow(2) \end{gathered}`

Now, we have a system of equations to solve it

Subtract equation (1) from equation (2) to eliminate b

`\begin{gathered} (11m-7m)+(b-b)=(122-82) \\ 4m+0=40 \\ 4m=40 \end{gathered}`

Divide both sides by 4 to find m

`\begin{gathered} (4m)/(4)=(40)/(4) \\ m=10 \end{gathered}`

Substitute m in equation (1) by 10 to find b

`\begin{gathered} 7(10)+b=82 \\ 70+b=82 \end{gathered}`

Subtract 70 from both sides to find b

`\begin{gathered} 70-70+b=82-70 \\ b=12 \end{gathered}`

The equation of the cost of L lessons is

`C=10L+12`

If the number of the lessons is 4, then substitute L by 4 to find the cost

`\begin{gathered} C=10(4)+12 \\ C=40+12 \\ C=52 \end{gathered}`

The cost of the 4 lessons is $52

11. C = 10L + 12

12. $52