gwen, tristan, and keith like to work out at the gym. they each have an app on their phone that estimates the calories they burn. by the time tristan and keith started exercising, gwen had already burned 100 calories. gwen burns 10 calories every minute, tristan burns 125 every 10 minutes, and keith burns 300 calories every 30 minutes. let x represent the number of minutes since tristan and keith started exercising and y represent the number of app-estimated calories burned.

1)write an equation representing gwen’s calories burned with respect to the number of minutes since tristan and keith started exercising.
2)write an equation representing the number of calories tristan has burned with respect to the number of minutes since he and keith started exercising.
heelp

Problem 1)

The equation is in linear form y = mx+b where 

m = slope = speed of calories burned (aka how many calories burned per minute)

b = y intercept = starting amount of calories burned

For Gwen, we have...
m = 10 because she burns 10 calories per minute
b = 100 because by the time Tristan and Keith start exercising, she has already burned 100 calories (she got a head start)

So we go from y = mx+b to y = 10x+100

The equation for Gwen is y = 10x + 100



Problem 2)

We'll use the same template y = mx+b as in problem 1

For Tristan, we have...

m = 12.5 since "Tristan burns 125 every 10 minutes" indicates his rate is 125/10 = 12.5 calories per minute

b = 0 because he starts off burning no calories at all

Why does he start at 0 when Gwen starts at 100? Well it's simply based on how x is defined. Recall that we "Let x represent the number of minutes since Tristan and Keith started exercising". So when x = 0, aka the starting time, Gwen is already 100 calories into her workout while Tristan is just getting started. There's no way Tristan can burn any calories at the very instaneous starting point.

Put simply, Gwen has got a head start which is why she burned 100 calories when x = 0.

So we will go from 
y = mx+b
to 
y = 12.5x+0
which simplifies to
y = 12.5x

The equation for Tristan is y = 12.5x