slope question help!?

Question

A group of mountain climbers begin an expedition with 265 lb of food. They plan to eat a total of 15 lb of food per day.
A. Write an equation in slope-intercept form relating the remaining food supply R, to the number of days D.
B Graph the equation ( if someone figures out the equation, i'll graph it)
C. The group plans to eat the last of their food the day their expedition ends. Use your graph ( I'll figure one out myself) to find out how many days they expect the expedition to last. How would I figure that out using the graph?? do i like count how high the graph went starting from 0,0??? PLZ HELP!

Answer 1

A)
R=265-15D

since 265 is the original, and 15 pounds times the number of days will give you the amount consumed in total, 265-15D will give you R, the amount of food remaining

C)
since 265 is the max they can eat, move it over to the other side.
-265 = -15D
negatives cancel (265=15D)
17.6666666...... = D
so they will have 17 days eating 15 pounds, and on the 18th day they will eat the remainder. this means they plan on the expedition lasting 18 days

Answer 2

15 pounds/day is a rate, hence is equivalent to a slope. Since you're consuming, the slope must be negative. At day=0, you have the full amount of food, hence the y-intercept is 265 lb.

Putting it together gives you remaining food = 265 lb - (15 lb/day)(x day).

Sometimes, carrying the units through helps you verify and make sense of the equation.

When the food runs out, that means there is no remaining food, hence 0 = 265 -15(total time) solve for total time. You can do the exact same time by finding the point on your plot where remaining food line intersects the x-axis, since that's when you have no remaining food. That's the x-intercept.

This is a perfect example of linear algebra applied to a relatively real-life problem. Knowing this, you can now plan hikes without running out of food!!

Answer 3

A. Let food left be R lb

Well after D days R = 265 - 15D (original amount less food used after D days)

B. To graph is easy Cuts R axis at 265 and slope is -15 ( ie slopes down and falls 15 for each increase of 1 D)

C. To find out expected length of expedition you need to establish when will R be 0 and that is when will the line cross the D axis.

Answer 4

A.R=265-15D

B.

C.putting R=0
D=265/15=53/3=17 1/3 days

Answer 5

wouldn't your equation be R=265-15*D ?
After 17 days, there would be 10 lbs of food left over for day 18.
(265-15*17 = 10)

Answer 6

In your graph, x is the time elapsed and y is the amount of food left.

At x=0, you have y=265. Plot a point at (0,265).

At x=1 there are 15 lbs less, so plot another at (1,250).

Keep going: (2,235), (3, 220) and so on...