Question

The coat for 7 dance lessons is $82 the cost for 11 lessons is $122 Write a linear equation slope-intercept form, to find the total cost C for L lessonsPart 2 Use the equation in #11 to find the cost of 4 lessons

Answer 1

Step 1:

Let y represent the cost C and let x represent the number of lessons.

Step 2:

Write the formula for two points forms of the equation of a linear equation.

`(y-y_1)/(x-x_1)\text{ = }(y_2-y_1)/(x_2-x_1)`

Step 3:

Write the given data

`\begin{gathered} x_1\text{ = 7} \\ y_1\text{ = 82} \\ x_2\text{ = 11} \\ y_2\text{ = 122} \end{gathered}`

Step 4:

Substitute the values in the formula

`\begin{gathered} \frac{y\text{ - 82}}{x\text{ - 7}}\text{ = }\frac{122\text{ - 82}}{11\text{ - 7}} \\ \frac{y\text{ - 82}}{x\text{ - 7}}\text{ = }(40)/(4) \\ \frac{y\text{ - 82}}{x\text{ - 7}}\text{ = 10} \\ \text{Cross multiply} \\ y\text{ - 82 = 10x - 70} \\ y\text{ = 10x - 70 + 82} \\ y\text{ = 10x + 12} \end{gathered}`

Step 5:

Write the equation

C = 10L + 12

Part 2

The cost for 4 lessons

L = 4, C = ?

From the equation C = 10L + 12

C = 10 x 4 + 12

C = 40 + 12

C = $52