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

Explanation:

Step1: Find constant pace

First, calculate the pace (minutes per kilometer) using the given data. Using the first set of values: $t=18$ minutes, $k=2$ km. Pace $=\frac{18}{2}=9$ minutes/km. This means $\frac{t}{k}=9$, or $t=9k$.

Step2: Use point-slope form

We use the point-slope formula for linear equations: $k - k_1 = m(t - t_1)$, where $m$ is the slope (kilometers per minute, reciprocal of pace). $m=\frac{1}{9}$, and we use the point $(t_1, k_1)=(18, 2)$.
Substitute into the formula:
$k - 2 = \frac{1}{9}(t - 18)$

Answer:

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