Take a moment to recap. What does this equation mean?

\( y \): This represents the total weight (in ounces) of the plate plus the pancakes.
\( x \): This represents the number of pancakes on the plate.
\( m = 1.5 \): 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.
\( b = 3.5 \): 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.

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.

GPT-4o mini · Answer

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.