wanting to cut down his television-watching time slowly, Vince decides to watch 30 fewer minutes of television each week after the first. If Vince watches 6 hours of television during the first week, which of the following equations predicts vince's hours of television n weeks after the first

f (n) = - 0.5n + 6

Step-by-step explanation:

Because Vince cuts down his television watching at a steady pace, his situation models a linear function. As such, we can use slope-intercept form to write and predict his hours watching tv in n weeks.

Slope-intercept form is y=mx+b. In this case, we are choosing to use f (n) instead of y to show the number of hours he is watching tv. We are also choosing to use n weeks instead of x. So we have the form f (n) = mn+b.

We know that Vince starts out at watching 6 hours a week. This is our initial value known as the y-intercept and represented by b. As each week passes, he will decrease from the previous week by 30 minutes or - 0.5 hours since 30 out of 60 minutes is 0.5. And since he is decreasing it should be a negative rate of - 0.5 and is represented by m.

We substitute b=6 and m=0.5 into our form to get f (n) = -0.5n+6. Let's test week 1. After 1 week he should be down from 6 hours to 5.5 hours or 5 hours and 30 minutes. Let's substitute n=1.

f (n) = -0.5 (1) + 6=-0.5+6=5.5

We can substitute for any n week and find the amount.