In order to write and solve linear equations, you need to understand what each piece of the equations stands for. "y=mx+b" is the slope intercept form of a line. We will only focus on this form as we write and solve linear equations since all other forms of a line come from this one.
"y" is the dependent variable. The dependent variable depends on the independent variable like a child depends on his/her parents. To understand if a variable is dependent ask yourself if you say "it depends". For example, if I asked you "How much money will Sarah make if her job pays $17 an hour?" You would respond, "It depends on how many hours she works". Therefore, the amount of money she makes is the dependent variable because it depends on how long she works. In this situation the y axis would represent dollars.
"x" is the independent variable. The independent variable just keeps going regardless of anything else. It is called independent because it is like an independent adult who doesn't rely on someone else to do things for him/her anymore. Referring to the previous example, time would be the independent variable because how long Sarah works does not rely upon her money. Time simply keeps ticking.
"m" is the slope. The slope of a line has been discussed in depth in other areas of this website. The slope is a rate of change. In a word problem you can find the slope by looking for the key words: each, every, in, or per. The slope is also thought of as the change in "y" over the change in "x". Graphically,it can be thought of as how you "move" on the graph.
"b" is the y-intercept. The y-intercept is where the line crosses (or intersects with) the y axis. In a word problem the y-intercept is the same as a fixed cost or something that only occurs once. It can be thought of as where you "begin" on when graphing a line.
Click on the following interactive power point below to learn more about writing and solving real world, linear equations.
In order to write and solve linear equations, you need to understand what each piece of the equations stands for. "y=mx+b" is the slope intercept form of a line. We will only focus on this form as we write and solve linear equations since all other forms of a line come from this one.
"y" is the dependent variable. The dependent variable depends on the independent variable like a child depends on his/her parents. To understand if a variable is dependent ask yourself if you say "it depends". For example, if I asked you "How much money will Sarah make if her job pays $17 an hour?" You would respond, "It depends on how many hours she works". Therefore, the amount of money she makes is the dependent variable because it depends on how long she works. In this situation the y axis would represent dollars.
"x" is the independent variable. The independent variable just keeps going regardless of anything else. It is called independent because it is like an independent adult who doesn't rely on someone else to do things for him/her anymore. Referring to the previous example, time would be the independent variable because how long Sarah works does not rely upon her money. Time simply keeps ticking.
"m" is the slope. The slope of a line has been discussed in depth in other areas of this website. The slope is a rate of change. In a word problem you can find the slope by looking for the key words: each, every, in, or per. The slope is also thought of as the change in "y" over the change in "x". Graphically,it can be thought of as how you "move" on the graph.
"b" is the y-intercept. The y-intercept is where the line crosses (or intersects with) the y axis. In a word problem the y-intercept is the same as a fixed cost or something that only occurs once. It can be thought of as where you "begin" on when graphing a line.
Click on the following interactive power point below to learn more about writing and solving real world, linear equations.