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

Write a linear equation, slope intercept form, to find the total cost of C for L lessons-example-1
User Rasmusx
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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

User Memetech
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