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.

Answer 1

So you're supposed to write the equation?

Answer 2

Points are (independent variable, dependent variable). For this problem that's (minutes, kilometers). So what are the two points you're given?

Answer 3

(18,2) (54,6)

Answer 4

yes. Do you know how to find the equation of a line through two points?

Answer 5

i'm not completely sure. can you walk me through it?

Answer 6

Start by finding slope
\[m=\frac{ y _{2} -y _{1}}{ x _{2} -x _{1} }\]

Answer 7

1/9 = slope

Answer 8

yes.
so the normal equation of a line is y = mx + b, but they switched you letters to k and t so your equation is k = mt + b.

Answer 9

Plug in m and one of the points for k and t and solve for b

Answer 10

k-2=1/9(t-18) ?

Answer 11

yes