1) Linear relationships are represented by the equation y=mx+b.

m stands for the rate of change and the coefficient of x. For example, a walking rate could be 2 meters per second.

y is the dependent variable, like distance, or the output.

x is the independent variable, like time, or the input.

b is the y-intercept, or the point where the line crosses the y axis on a graph or when 0 is y in a table.

If you were to plot the equation y=mx+b (when the letters are numbers) then the line should be a straight line, meaning it’s linear.

2a) You can use a table or graph for a linear relationship to solve a problem. You can use the information on a table to solve a problem. You can use a graph because if the line is linear, you can use the scale marks and the information on it to solve a problem.

2b) I have used an equation to solve a problem in many ways. I have used the guess and check method using equations by putting a number that is an estimate and seeing if it works. I have also learned to find a number that intersects 2 equations by having 2 equations on either side of an equal sign. For example, in problem 3.5, there were two equations: E=825+3.25n and I=8.20n. Then I did 825+3.25n=8.20n then just solved the equation.