Answer:
See below
Step-by-step explanation:
First you need to remember the slope intercept model equation is
y = mx + b
m is the slope of the line and b is the point where the line intersects the y axis which means when x = 0
Let's start with the x and y variables. We can use y to designate the total cost of the party. Then we can use x to represent the number of guests. Based on that, y will increase when x increases.
Now look at your scenario. She is buying just one cake no matter how many guests there are. We said x was going to be the variable for the number of guests. So x (the number of guests) does not change how many cakes are bought. So we can use the cost of the cake as b. Why?
Because if 0 guests show up meaning x = 0, she is still going to buy 1 cake. So the cost of the cake actually is the y intercept. Remember the y intercept is the value of y when x = 0. Looking at y = mx + b, when x=0, y = b or the cost of the 1 cake.
So far we have y = mx + 24.99 where x equals the number of guests.
How much with the total cost increase for each guest? The cost of one ice cream which is 2.49. So if x = 1, y increases by 2.49. If x = 2, y increases by 4.98 and so on.
You should be able to see then that the slope (m) is actually the cost of the ice cream. When you take the cost of the ice cream (m) times the number of guests (x), y will increase as we said above as x keeps increasing.
Putting it all together, you would have:
y = 2.49x + 24.99
2.49 is m which is the slope and the ice cream cost
24.99 is b which is the y intercept or the point on the y axis when x = 0 and the cost of the 1 cake.
y is the total cost of the party
x is the number of guests
