Answer:
[tex]y = -\frac{1}{5}x + 5[/tex]
Step-by-step explanation:
Given
[tex]5\ minutes = 4\ miles[/tex]
[tex]15\ minutes = 2\ miles[/tex]
Required
Determine the equation
y represents distance
x represents time
So, the given parameters can be modeled (x,y) as:
[tex](x_1,y_1) = (5,4)[/tex]
[tex](x_2,y_2) = (15,2)[/tex]
First, we need to determine the slope of the function.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{2 - 4}{15 - 5}[/tex]
[tex]m = \frac{-2}{10}[/tex]
[tex]m = -\frac{1}{5}[/tex]
The equation can be determined using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = -\frac{1}{5}[/tex]
[tex](x_1,y_1) = (5,4)[/tex]
[tex]y - y_1 = m(x - x_1)[/tex]
becomes
[tex]y - 4 = \frac{-1}{5}(x - 5)[/tex]
Open bracket
[tex]y - 4 = -\frac{1}{5}x + 1[/tex]
Solve for y
[tex]y = -\frac{1}{5}x + 1 + 4[/tex]
[tex]y = -\frac{1}{5}x + 5[/tex]
