julissa is running a 10 - kilometer race at a constant pace. after running for 18 minutes, she completes 2…

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

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

Answer

Explanation:

Step1: Calculate the speed

Since she runs 2 kilometers in 18 minutes, the speed $v=\frac{2}{18}=\frac{1}{9}$ kilometers per minute.

Step2: Use the point - slope form of a linear equation

The point - slope form of a line is $y - y_1=m(x - x_1)$. Here, $t$ is the independent variable (like $x$) and $k$ is the dependent variable (like $y$). We have a point $(t_1,k_1)=(18,2)$ and slope $m = \frac{1}{9}$. Substituting into the point - slope form gives $k - 2=\frac{1}{9}(t - 18)$.

Answer:

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