SOLUTION: Amy is driving her car to a conference . The expression d = 65t + 100 represents her total distance from home in miles, and t is the number of hours since 8:00 AM. How many mile

Question 1125527: Amy is driving her car to a conference . The expression d = 65t + 100 represents her total distance from home in miles, and t is the number of hours since 8:00 AM.
How many miles will Amy be at 12:00 noon?
What does d-intercept represent in this problem?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the equation is 65 * t + 100
t is the number of hours since 8:00 am.
d is her distance from home.

at 12:00 noon, she has been on the road for 4 hours (12 - 8 = 4).

d = 65 * t + 100 becomes d = 65 * 4 + 100 which becomes d = 260 + 100 which results in d = 360 miles from home.

the d-intercept would be the value of d when t = 0.

when t = 0, the equation becomes d = 65 * 0 + 100 which results in d = 100.

in context of this problem, i believe this means she was already 100 miles from home when she started at 8:00 am.

this might be easier to see if you let y = d and you let x = t.

the equation then becomes y = 65 * x + 100.

the d-intercept now becomes the y-intercept, which is the value of y when x = 0.

you can graph the equation of d = 65t + 100 by replacing d with y and t with x.

the graph looks like this.

$$$

the blue line is the graph of the equation.

the orange lines are there to show the intersection points of the equation when x = 0 and x = 4.

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