Question

On a snow day, Leah created two snowmen in her backyard. Snowman A was built to a height of 36 inches and Snowman B was built to a height of 60 inches. The next day, the temperature increased and both snowmen began to melt. At sunrise, Snowman A's height decrease by 3 inches per hour and Snowman B's height decreased by 9 inches per hour. Let
A
A represent the height of Snowman A
t
t hours after sunrise and let
B
B represent the height of Snowman B
t
t hours after sunrise. Graph each function and determine how tall each snowman is when they are the same height.

Answer 1

Let's first determine each function

We want to write the equations in the slope-intercept form because that's the easiest way especially with the information they've given us

Recall that the slope-intercept form is
y = mx + b

where m is the slope
and b is the y-intercept

Now, for your question they've asked us to use different variables
A is our height
and t is the time

so let's re-write the slope intercept form as

A = mt + b

We need to come up with 2 equations for our 2 snowmen

m, or slope, is the rate of change. It's the number that tells us how much the height (A) is increasing or decreasing by at a given time (t)
b, or y-intercept, is going to be the initial height that we have before the snowman starts melting

Answer 2

So I'll show you how to come up with the first equation to get you started

Snowman A is 36 inches and its height decreases by 3 inches per hour

The height is decreasing by 4 inches per hour. The keyword here is decreasing This means that our rate of change or slope or m is NEGATIVE 3 or -3.
Snowman A started off with a height of 36 inches so that's our y-intercept

So what's our final equation for snowman A?

A = mt + b
we said m is -3 and b is 36 so we get

A = -3t + 36

Now can you come up with the equation for snowman B?
Your question says:
Snowman B was built to a height of 60 inches and Snowman B's height decreased by 9 inches per hour

What's our slope and what's our y-intercept?
And can you put it into A = mt + b like I did for the previous snowman?

Answer 3

Once you get that, it's time to graph it!

We can use this handy dandy graphing calculator: https://www.desmos.com/calculator

If you want to find out when they're the same height, you have to look for when the two lines cross each other. That's going to tell you the time when they're both the same height.
Remember the point where they intersect or cross each other is in the form of (x, y) or in our case (t, A)
so the y-value is going to be the height when the two snowmen are the same height