1. In the equation y = mx + b, the rate is expressed by the variable “m”. The y-intercept, which is the point where the line crosses the y axis on a graph or when y equals 0 in a table, is expressed by the variable “b”. Also, the y intercept is what is added to the rate or coefficient. Next, the dependant variable, for example, distance, is expressed by “y”. The coefficient is the number that multiplies a variable in an equation. Finally, the independent variable, for example, time, is expressed by the variable “x”.

2. a) A table or graph for a linear relationship can be used to solve a problem by filling in the table or graph and finding the numbers you need to do the problem. For example, if Lucy buys 20 apples for $4.00 each, and you need to figure out how much each apple cost, you can use a table and/or a graph. To use a table, take the equation and rate to find the numbers used in the table. Then continue the table to find your answer. The x column on the table would show that it is $5 for one apple. You can do the same thing with a graph, but just extend the line on the graph until you have your answer.

b) To solve a problem using the equation, substitute the real numbers from the problem for the variables. For example, if we had the same situation with Lucy and her apples the equation would be C = 5n, (c is the total cost and n is the number of apples) so substitute how many apples you need to find, lets say 3, and compute the equation.