Question

julissa is running a 10 - kilometer race at a constant pace. after running for 18 minutes, she completes 2 kilometers. after running for 54 minutes, she completes 6 kilometers. her trainer writes an equation letting t, the time in minutes, represent the independent variable and k, the number of kilometers, represent the dependent variable. which equation can be used to represent k, the number of kilometers julissa runs in t minutes? \\(k - 18 = \frac{1}{9}(t - 2)\\) \\(k - 2 = 9(t - 18)\\) \\(k - 18 = 9(t - 2)\\) \\(k - 2 = \frac{1}{9}(t - 18)\\)

Explanation:

Step1: Find the slope (rate)

The slope \( m \) between two points \((t_1, k_1) = (18, 2)\) and \((t_2, k_2) = (54, 6)\) is calculated as \( m=\frac{k_2 - k_1}{t_2 - t_1}=\frac{6 - 2}{54 - 18}=\frac{4}{36}=\frac{1}{9} \).

Step2: Use point - slope form

The point - slope form of a linear equation is \( y - y_1=m(x - x_1) \). Here, using the point \((18, 2)\) (where \( x_1 = t_1 = 18 \) and \( y_1=k_1 = 2 \)) and \( m=\frac{1}{9} \), we substitute into the formula. Let \( k=y \) and \( t = x \), so the equation becomes \( k - 2=\frac{1}{9}(t - 18) \).

Answer:

\( k - 2=\frac{1}{9}(t - 18) \)