Respuesta :
Answer:
(a) [tex]y = 0.025x+15[/tex]
(b) 18.5 minutes
(c) 450.4 minutes
Step-by-step explanation:
Given
[tex]290\ minutes = \$22.25[/tex]
[tex]360\ minutes = \$24.00[/tex]
Solving (a): Determine the linear equation
First, we need to calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (290,22.25)[/tex]
[tex](x_2,y_2) = (360,24.00)[/tex]
So, we have:
[tex]m = \frac{24.00 - 22.25}{360 - 290}[/tex]
[tex]m = \frac{1.75}{70}[/tex]
Multiply through by 100
[tex]m = \frac{1.75 * 100}{70 * 100}[/tex]
[tex]m = \frac{175}{7000}[/tex]
Next, is to calculate the equation of the line using:
[tex]y - y_1 = m(x - x_1)[/tex]
Recall that:
[tex](x_1,y_1) = (290,22.25)[/tex]
[tex]m = \frac{175}{7000}[/tex]
[tex]y - 22.25 = \frac{175}{7000}(x - 290)[/tex]
[tex]y - 22.25 = \frac{175x}{7000} - \frac{175}{7000} * 290[/tex]
[tex]y - 22.25 = \frac{175x}{7000} - \frac{50750}{7000}[/tex]
Add 22.25 to both sides
[tex]y = \frac{175x}{7000} - \frac{5075}{700} + 22.25[/tex]
[tex]y = \frac{175x}{7000} + \frac{-5075 + 15575}{700}[/tex]
[tex]y = \frac{175x}{7000} + \frac{10500}{700}[/tex]
[tex]y = 0.025x+15[/tex]
(b) Solve for y when x = 140
[tex]y = 0.025x+15[/tex]
Substitute 140 for x
[tex]y = 0.025 * 140 + 15[/tex]
[tex]y = 3.5 + 15[/tex]
[tex]y = 18.5[/tex]
(c) Solve for x when y = 26.25
[tex]y = 0.025x+15[/tex]
Substitute 26.25 for y
[tex]26.25 = 0.025x + 15[/tex]
Solve for 0.025x
[tex]0.025x = 26.26 - 15[/tex]
[tex]0.025x = 11.26[/tex]
Solve for x
[tex]x = 11.26/0.025[/tex]
[tex]x = 450.4\ minutes[/tex]