Question

Assume a 125 pound person burns 150 calories after 15 minutes of jogging and 200 calories after 20 minutes of jogging.

Part 1: Use calories as the y-coordinate and minutes as the x-coordinate. After writing two ordered pairs, find the slope. What does the slope represent in terms of the information provided?

Part 2 : Write an equation, in slope intercept form, to represent this data.

Part 3 : How many calories will this person burn after 35 minutes of jogging? Using complete sentences, explain how the equation, slope, or graph can help to predict calories burne

Answer 1

@satellite73 help please.

Answer 2

Slowly please. One part at a time.

Answer 3

ok

Answer 4

one point on both of these lines is (0,0) because if you do not jog, you do not burn any calories (at least in this set up)

Answer 5

first one
Assume a 125 pound person burns 150 calories after 15 minutes
one point on your graph is the origin, (0,0) and the other is (15,150) because they have told you that minutes is the \(x\) and calories is the \(y\)

Answer 6

now computing the slope here is easier than before, because you can ignore the (0,0) point. the slope in this case is simply \(\frac{y}{x}=\frac{150}{15}=10\)

Answer 7

also notice that \(\frac{200}{20}=10\)

Answer 8

So the slope is 200/20=10

Answer 9

and that \[\frac{200-150}{20-15}=\frac{50}{5}=10\] so your slope it 10 for sure

Answer 10

i think they want you to write the two ordered pairs as
\[(15,150) \text{ and } (20,200)\]

Answer 11

then they ask
What does the slope represent in terms of the information provided?
this is the unit rate, in other words the slope is calories per minute

Answer 12

SO what would I write for part 1?

Answer 13

ok lets write what they want.
a) two ordered pairs are (15,150) and (20,200)
b) slope is \(\frac{200-150}{20-15}=\frac{50}{5}=10\)
c) the slope represents the unit rate, calories per minute

Answer 14

that takes care of part 1

Answer 15

ok?

Answer 16

Okay one second please.

Answer 17

k

Answer 18

Okay ready for part two.

Answer 19

Part 2 : Write an equation, in slope intercept form, to represent this data.

ok before we begin, lets know what the answer is. the slope is 10, and the \(y\) intercept is 0 (because if we do not jog, we do not burn calories), so the answer is \(y=10x\) but also we can compute

Answer 20

again we use the "point - slope" formula (your favourite ) \[y-y_1=m(x-x_1)\] and we can use it with \(m=10,x_1=20 y_1=200\) to get
\[y-200=10(x-20)\]

Answer 21

now multiply out and get
\[y-200=10x-200\] add 200 to both sides and get
\[y=10x\] as promised

Answer 22

ok?

Answer 23

So what would I all write for part 2?

Answer 24

\[y-200=10(x-20)\]
\[y-20=10x-200\]
\[y=10x\] should do it

Answer 25

Part 3 : How many calories will this person burn after 35 minutes of jogging? Using complete sentences, explain how the equation, slope, or graph can help to predict calories burn?

Answer 26

since our equation is \(y=10x\) where \(y\) represents calories and \(x\) represents minutes, if we want to predict how many calories are burned in 35 minutes, replace \(x\) by 35 and find \(y\) i.e. multiply by 10
you get \(y=10\times 35=350\) calories in 35 minutes

Answer 27

and that is that

Answer 28

on line class, summer school, home school?

Answer 29

Online class.
I was in a slow math class so I just took regular online math and I need to pass it. I'm so behind. Thank you sooooo much for your help!

Answer 30

yw, don't stay up all night doing it

Answer 31

Lol. I just finished my exam. (:

Answer 32

yay!!!