Question

Take a moment to recap. What does this equation mean?
x
y
(1,5)(3,8)
0
1
2
3
4
5
0
1
2
3
4
5
6
7
8
9
10
11
12
Number of pancakes
Total weight (oz)
y
=
mx + b
y
=
1.5x + 3.5


The plate weighed
ounces when there were 0 pancakes, and each pancake added a weight of
ounces.

Answer 1

The equation you provided, \( y = 1.5x + 3.5 \), describes a linear relationship between the number of pancakes \( x \) and the total weight \( y \) in ounces.

Here’s a breakdown of what each part of the equation means:

1. **\( y \)**: This represents the total weight (in ounces) of the plate plus the pancakes.
2. **\( x \)**: This represents the number of pancakes on the plate.
3. **\( m = 1.5 \)**: This is the slope of the line, which indicates that each pancake adds 1.5 ounces to the total weight. So, for every pancake you add (\( x \) increases by 1), the total weight (\( y \)) increases by 1.5 ounces.
4. **\( b = 3.5 \)**: This is the y-intercept, meaning that when there are 0 pancakes on the plate (\( x = 0 \)), the total weight of the plate (without pancakes) is 3.5 ounces.

### Summary
- The plate starts at a weight of 3.5 ounces when there are no pancakes.
- Each additional pancake adds 1.5 ounces to this weight.

Thus, to find out the total weight for any number of pancakes, you simply plug in the value of \( x \) into the equation. For example, if you have 4 pancakes, the total weight would be:

\[
y = 1.5(4) + 3.5 = 6 + 3.5 = 9.5 \text{ ounces}
\]

This equation succinctly illustrates how the total weight changes as you add pancakes.