Explain what the slope and \(y\)-intercept mean in each situation.

1. 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.
2. 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.
3. The number of chapters read, \(y\), after \(x\) days. The slope of the line is \(\frac54\) and the \(y\)-intercept is 2.
4. 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.

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.

1. What does the slope of the line shown by the points mean in this situation?
2. 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. Points include 0 comma 60, 1 comma 80, 2 comma 100, 3 comma 120, 4 comma 140, 5 comma 160, 6 comma 180, 7 comma 200.

The graph shows the relationship between the number of cups of flour and the number of cups of water in a recipe for making tortillas.

Recipe 1:

graph, horizontal axis, cups of water, scale 0 to 5, by 1's. vertical axis, cups of flour, scale 0 to 12, by 3's. points plotted at 1 comma 3, 2 comma 6, 3 comma 9 , 4 comma 12.

The table shows the amounts of flour and water needed for a different tortilla recipe.

Recipe 2:

flour (cups)	water (cups)
\(2\frac12\)	1
5	2
\(7\frac12\)	3

1. How much flour is needed for each recipe if 6 cups of water are used?
2. How much water is needed for each recipe if 5 cups of flour are used?

Solve each of these equations. Explain or show your reasoning.