Lesson 6
More Linear Relationships
Let’s explore some more relationships between two variables.
Problem 1
Explain what the slope and intercept mean in each situation.
- A graph represents the perimeter, \(y\), in units, for an equilateral triangle with side length \(x\) units. The slope of the line is 3 and the \(y\)-intercept is 0.
- The amount of money, \(y\), in a cash box after \(x\) tickets are purchased for carnival games. The slope of the line is \(\frac14\) and the \(y\)-intercept is 8.
- The number of chapters read, \(y\), after \(x\) days. The slope of the line is \(\frac54\) and the \(y\)-intercept is 2.
- The graph shows the cost in dollars, \(y\), of a muffin delivery and the number of muffins, \(x\), ordered. The slope of the line is 2 and the \(y\)-intercept is 3.
Problem 2
Customers at the gym pay a membership fee to join and then a fee for each class they attend. Here is a graph that represents the situation.
- What does the slope of the line shown by the points mean in this situation?
- What does the vertical intercept mean in this situation?
![Points plotted. Horizontal axis, number of classes, scale 0 to 8, by 1’s. Vertical axis, cost in dollars, scale 0 to 200, by 20’s.](https://cms-im.s3.amazonaws.com/f4uShvLo6u9rcSMm3pPaM12d?response-content-disposition=inline%3B%20filename%3D%228-8.3.B6.PP.graph3.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.B6.PP.graph3.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233121Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b1e6b4b97c5e77a466e113347ae1d13901823e25ff9ec09284da6d2887817a27)
Problem 3
The graph shows the relationship between the number of cups of flour and the number of cups of sugar in Lin’s favorite brownie recipe.
![graph, horizontal axis, cups of sugar, scale 0 to 5, by 1's. vertical axis, cups of flour, scale 0 to 4, by 1's.](https://cms-im.s3.amazonaws.com/DdHeh3A7BgED1wZTZSy4rGoy?response-content-disposition=inline%3B%20filename%3D%228-8.3.A4.PP.brownies.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.A4.PP.brownies.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233121Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=29a1f41eab6c8a6021bfedb259cdb2babf67b86d0a217f003d09c6eb6207a5f9)
The table shows the amounts of flour and sugar needed for Noah’s favorite brownie recipe.
cups of sugar | cups of flour |
---|---|
\(\frac32\) | 1 |
3 | 2 |
\(4\frac12\) | 3 |
- Noah and Lin buy a 12-cup bag of sugar and divide it evenly to make their recipes. If they each use all their sugar, how much flour do they each need?
- Noah and Lin buy a 10-cup bag of flour and divide it evenly to make their recipes. If they each use all their flour, how much sugar do they each need?