Given:
Connor runs at a constant rate.
It takes him 34 minutes to run 4 miles.
To find:
The linear equation in two variables that represents the given situation.
Solution:
Let y be the distance covered by Connor in miles and x be the time in minutes.
It is given that Connor needs 34 minutes to run 4 miles. So, the linear equation passes through the point (34,4,) and the rate of change is:
[tex]m=\dfrac{Distance}{Time}[/tex]
[tex]m=\dfrac{4}{34}[/tex]
Using the point slope, the equation of the linear function is:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-4=\dfrac{4}{34}(x-34)[/tex]
[tex]y-4=\dfrac{4}{34}x-4[/tex]
[tex]y=\dfrac{4}{34}x[/tex]
Therefore, the correct option is D, i.e., [tex]y=\dfrac{4}{34}x[/tex].
