How to Use Graphs Effectively
Improper Fractions and Mixed Numbers
Many times, you can use a graph to represent data in a more organized way, and in a more visual way. Say we have the equation y equals 2x minus 3. What can do is plug in a couple of numbers for x and then find out what number we get for y, and then we can come out with some coordinates plug them in here, and then draw a line representing the values of this equation.
We’re going to start out by plugging in 0 for x. I’m just going to put parentheses like that. 2 times 0 is 0, minus 3, equals -3, so y equals -3. The first coordinate we get is x equals 0 and y equals -3. We’re going to plug in 5 for x, so we’re going to put 5 in parentheses.
We get 10 minus 3 equals 7, so y equals 7. In this case x equals 5, y equals 7. We have these two coordinates you just plug these in to this graph right here, and we can get a line. We have these dash marks here. I need to go ahead and label these, so we have this x axis, which runs horizontal, left to right.
Then we have the y axis, which runs vertical, or up and down. On the right side of the y axis the x axis is positive, and on the left side it is negative. This works similarly for the y axis. Above the x axis it’s positive, and below it’s negative. First, we’re going take a look at this coordinate right here.
We have the x coordinate and the y coordinate, we find x first which is 0, so we are right here. Then we go down to -3 and draw a dot, and I’m going to go ahead and put the coordinates right there. Then we look for the x coordinate first and then the y coordinates.
We find 5, then we need to go all the way up to 7, we’re going to need to extend this line a little bit to make it up there. We’re going to go from 5 all the way up to 7 and draw a dot. Then we just need to draw a line all the way up there.
If you’re using a piece of paper, you can often use a ruler, so I’m just going to attempt to freehand this which means the line is not going to be very straight as you can see, but we do need to draw the coordinates -or write the coordinates for that too. Then we have a line, and you can go all the way up this line and see different points on it.
You can go “Oh okay, if x equals this certain number, then y is equal this certain number.” Because you can follow it across here, you can go down and find the x coordinate, and then go across and find the y coordinate to figure out some other coordinates here, or to figure out some other values for x and y. Here you just have coordinates written on a page. It may not mean much to you, it’s hard to visualize what that looks like. Here you have a real visual format, real organized way to view a lot of data, and then be able to keep it and comprehended.