Answer:
Option D is correct
[tex]y =-\frac{1}{4}x+10[/tex]
Step-by-step explanation:
Slope intercept form:
The equation of line is given by:
[tex]y=mx+c[/tex] .....[1]
where, m is the rate or slope and c is the y-intercept or initial value.
As per the statement:
Here, y represents the distance in kilometer and x represents the time in minutes.
A student is running a 10-kilometer race
⇒y(0) = b = 10 km
It is also given that he runs 1 kilometer every 4 minutes.
Now, with each passing minute the student is getting closer and closer to the finish line which was 10 kilometers away when the race started. Thus, as the race progresses, the distance between the student and the finish line will decrease.
[tex]m =-\frac{1}{4}[/tex]
Substitute these in [1] we have;
[tex]y = -\frac{1}{4}x+10[/tex]
Therefore, the function that describes his distance from the finish line is, [tex]y = -\frac{1}{4}x+10[/tex]
