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.
[tex]\frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]
Step 3:
Write the given data
[tex]\begin{gathered} x_1\text{ = 7} \\ y_1\text{ = 82} \\ x_2\text{ = 11} \\ y_2\text{ = 122} \end{gathered}[/tex]
Step 4:
Substitute the values in the formula
[tex]\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{ = }\frac{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}[/tex]
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
