Thread: Graphing Linear Equations:

I am starting all over on Math, after many years, and I'm having trouble with a question that was given to the class. I have read it a few times and it is not clicking with me yet. Is there anyone that can explain it in a simpler way, so that I can grasp it. Thank you.

Consider this equation, y= ax + b. When you are given an actual linear equation, you're almost always given something where the a and b have been replaced with actual numbers so you typically see equations like y=3x+2 and so on. The x and y are pretty much always there to taunt you so here are 3 questions to answer based on this and to get you rooted in graphing linear equations:

1) How can you choose x values to plug into a linear equation, like y=3x+2, so that you can graph it?
2) Related to 1), what if I told you that x is the independent variable and y is the dependent variable? How could you explain those definitions to someone else (knowing what you generally know about the terms independent (skate punk) and dependent (lives with mom still))?
3) The book tells us about two points that you can plot for a linear equation called the intercepts. What can you glean from the two points they give you in that paragraph (for Example 2) that will always help you solve for the intercepts? It has to do with the one value those two points have in common...

These are very strangely worded questions. I think they are trying to challenge you to do some thinking, or to present the material in an interesting way, but they could have been a little clearer.

I believe question 1 is asking you which x values might make the line easy to graph. For example, if you put something like -59.23 for the value of x in , you will find the resulting point (-59.23, -175.69) very annoying to graph. But if you put in integers which are fairly small (like -2, -1, 0, 1, 2, etc.), you will find y both very easy to calculate and to graph. If the function is something like , then it would be wise to choose x-values which are perfect squares (like 4, 9, 16, etc.) so that the resulting y-values will be integers. So generally, you would want to pick values for x such that the resulting value for y will be a low integer.

The question might also be asking what the minimum amount of information you would need to graph something is. Well, you need at least two points to graph a line, so you would preferably choose two low x-values which result in low integer y-values.

Question 2 seems to just be asking you the meaning of the words "independent" and "dependent". Well, the equation is written in such a way that you can plug in any value for x that you want and then calculate the corresponding y-value. So, since the y-value depends on what you chose for the x-value, we call y the dependent variable.

For question 3, the intercepts are the points where the line crosses the x- or the y-axis. I imagine that your book has given you something like for the x-intercept and for the y-intercept. The point the intercepts always have in common is zero: the x-intercept has 0 for the y-coordinate, and the y-intercept has 0 for the x-coordinate. To solve for the x-intercept, you let y equal 0 and solve for x. To solve for the y-intercept, you let x equal zero and solve for y.

Congratulations on starting over on math! I am doing much the same thing. Good luck!

Originally Posted by skyblu

I am starting all over on Math, after many years, and I'm having trouble with a question that was given to the class. I have read it a few times and it is not clicking with me yet. Is there anyone that can explain it in a simpler way, so that I can grasp it. Thank you.

Consider this equation, y= ax + b. When you are given an actual linear equation, you're almost always given something where the a and b have been replaced with actual numbers so you typically see equations like y=3x+2 and so on. The x and y are pretty much always there to taunt you so here are 3 questions to answer based on this and to get you rooted in graphing linear equations:

1) How can you choose x values to plug into a linear equation, like y=3x+2, so that you can graph it?

The easiest way is to let x = 0 and solve for y. This gives the point where the line crosses the y axis (y intercept)
Then let y = 0 and solve for x. This gives the point where the line crosses the x axis (x interpcept). Then you can draw a staight line between these two points.

Alternatively, just substitute in integer values of x and see what you get for y.

2) Related to 1), what if I told you that x is the independent variable and y is the dependent variable? How could you explain those definitions to someone else (knowing what you generally know about the terms independent (skate punk) and dependent (lives with mom still))?

These terms come from physics. In an experiment, you usually isolate an independent variable to test and keep the other variables constant. This enables you to test the effect of the independent variable on whatever you're trying to test. The dependent variable is the variable you'll be using to measure the effect of this change.

For example, if you wanted to see how the length of a pendulum affects it's period, you'll use length of the pendulum as the indepdent variable and the time it takes to complete one oscillation as the dependent variable.

Graphically you'll usually choose the independent variable as the x axis and dependent as the y axis. So the value of y depends on the value of x.

3) The book tells us about two points that you can plot for a linear equation called the intercepts. What can you glean from the two points they give you in that paragraph (for Example 2) that will always help you solve for the intercepts? It has to do with the one value those two points have in common...

See my response to Q1

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Thank you Ragnarok and Gusbob!!

I appreciate your reply's to my post for math help. I have been reading in my math book, and what you have both said, but I have come to the conclusion that I'm to tired to process tonight. It is after midnight. I will start fresh in the morning. Thank you for the time and explanation you have given me.

No problem. This stuff is hard to get back into at first. I had to search a long time for books that were easy enough for me to understand on my own, but interesting and challenging enough to keep my attention. What I found that helps if you keep butting your head against something is to consult that section in another book, or to skip to a section that you do understand and come back later. And, of course, a good night's sleep always helps.

Thanks again. Sometimes I have to read something over and over again before it finally clicks, also asking for help gives you a different view that makes more sense then what you are reading in a book. I appreciate your time.