Linear Relationships
I am going to show you a linear relationship with a graph, table and equation. Children are selling lemonade at a lemonade stand. A cup of lemonade is .50 cents (the slope), plus .25 for the cup (y-intercept).
Linear Graph
![Picture](/uploads/5/9/7/0/59700733/1096644.jpg?1444864111)
This is a graph of the lemonade sales. I know that it is linear because as the number of cups of lemonade you buy increases, the price increases. So the graph goes up at a constant rate starting at the y-intercept which is .25. You can also tell because it is a straight line, which means that it has a positive slope. The slope is .50/1 because it rises .50 units and goes right unit. Linear graphs can also have a negative slope, if the x and y values decrease.
Linear Table
![Picture](/uploads/5/9/7/0/59700733/8288525.jpg?1444864809)
This is a linear table of lemonade sales and prices. I know it is linear because it has a constant rate of change in the price and amount sold. You can see that .25 is the y-intercept because it was what y (price) equals when x (amount) equals zero. When you look at the variables you can see that they both increase at a constant rate. All this information tells you that it is a linear table.
Linear Equation
![Picture](/uploads/5/9/7/0/59700733/223173.jpg?420)
This is a linear equation. I know it is linear because it the base of it is y=mx+b. The y is the dependent variable, the m is your slope or rise over run, x is the independent variable, and the b is your y-intercept, which is what y equals when x equals zero. I just filled in the numbers from the graph and/or table to create this equation.
Parent Problem
Reflection
When I studied linear equations this year I understood it much better than last year. It just made more sense the more we talked about it, last year I got confused with it and I thought it was pretty hard but now I would even say that it's easy. I included this to help explain that math might be hard to understand at first, but it gets easier as you get more used to it. Math has never been my favorite but at least I understand how to do it now.