1. There is a linear relationship in the form of the equation y=mx+b. A linear relationship is when two variables form a constant rate of change. Y is the unknown, x is the unknown, m is the coefficient of x (the coefficient is the number that multiplies a variable in an equation) , and b is the y-intercept (the y-intercept is the point where the line crosses the y-axis). For example: if m=6 and b=5, the equation would be y=6x+5. Assuming that x=2, y would equal 17 because
y=6(2)+5.
y=12+5
y=17

check:
17=6(2)+5
17=12+5
17=17

If you had the value of y, which is 17, and needed to find the value of x, you would have the equation
17=6x+5.
-5 -5
-------
12=6x
/6 /6
-----
2=x

check:
17=6(2)+5
17=12+5
17=17

2.a. A table or graph can be used to solve a problem by evaluating the data. For a table, you can write an equation from the given data.


Prices for Tom's Bagels
|---------------------|----|----|----|----|----|----|
|# of Bagels....... | 1 | 2 | 3 | 4 | 5 | 6 |
|---------------------|----|----|----|----|----|----|
|Cost in cents.... |.25 |.50 |.75 |1.00|1.25|1.50|
|---------------------|----|----|----|----|----|----|

n=number of bagels c=cost in cents

c=.25n

A graph for a linear relationship can be used to solve a problem by evaluating the graph and finding plotted points on it that run within the linear line.


2.b. I have used an equation to solve a problem many times before. When some of my friends and I sold cupcakes at the seventh grade lunch, we estimated how much money we would raise for Haiti depending on how many cupcakes we made and depending on the price of each cupcake. If the cupcake was .25 cents and we made 75 cupcakes, we would raise $18.75. The equation is:

n=number of cupcakes m=money raised in dollars and/or cents

m=.25n