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3) In order to attend plays at the Ford Theater, Mr. Vajda pays a fee tobecome a member. In addition, he pays a set rate per play that he attends.After seeing 3 plays he has paid a total of $154.50, and after seeing 6 plays hehas paid a total of $300.50. Write a linear equation that gives the total cost, c,a member such as Mr. Vajda pays to see p plays?

Answer :

Givens.

• He paid $154.50 for 3 plays.

,

• He paid $300.50 for 6 plays.

First, form coordinate pairs: (3, 154.50) and (6, 300.50).

Second, find the slope between the points.

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}=\frac{300.5-154.5}{6-3} \\ m=\frac{146}{3} \end{gathered}[/tex]

The slope is 146/3.

Then, we use the point-slope formula to find the equation.

[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-154.5=\frac{146}{3}(x-3) \\ y-154.5=\frac{146}{3}x-146 \\ y=\frac{146}{3}x-146+154.5 \\ y=\frac{146}{3}x+8.5 \end{gathered}[/tex]

Therefore, the equation is

[tex]y=\frac{146}{3}x+8.5[/tex]

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