2-1 Proportional Relationships, Lines and Linear Equations
Overview: A video game store has a frequent shopper program. You earn 4 points for
every video game you buy. Draw a graph to model this situation.
You need 48 points for a free game. How many video games do you need to buy to have
enough points for a free game?
Solution!!
For every game you buy, you earn 4 points. Since you can only buy entire games, it only
makes sense to plot points with x coordinates that are whole numbers. For each point
on the graph, the y-coordinate should be four times the x coordinate.
Since you need 48 points for a free game, look for a point on the graph until you reach
a y coordinate of 48.
Key Concepts
Table-­‐ a table shows a proportional relationship when one quantity is a constant multiple of the other quantity. Graph-­‐ a graph shows points with a proportional relationship if a line that passes through the origin can be drawn though the points. (For each point the y-­‐coordinate is a constant multiple of the x-­‐coordinate.) Equation-­‐ equations in the form y=mx represent relationships. In the equation, m is the !
constant of proportionality or the constant multiple ! Sometimes a k is used to represent the constant of proportionately. So an equation in the form y=kx is the same as an equation in the form y=mx Part 2
A salesperson earns a 10% commission on sales of energy efficient appliances. Make a table and draw a graph to model this situation. Is the amount of the commission proportional to the amount of sales? How do you know? Solution:
Part 3:
Ice forms at 0℃ . The surface temperatures of the ice on an ice rink decreases .5° C every hour. Write an equation that models the temperature y after x hours. Then draw a graph to model this situation. Start when the surface temperature of the ice is 0° C. Is the surface temperature of the ice proportional to time? How do you know? Table
Equation:
Table
Equation
Solution