Graphs of Linear equations

Linear equations and graphs

Now that you have your points, you need to draw your axes. REMEMBER TO USE YOUR RULER! If you don’t use a ruler, you will have messy axes and inconsistent scales on the axes, and your points will NOT line up properly. Don’t “fake it” with your graphs. Get in the habit now of drawing neatly. It will save you so much trouble down the line! (And, no, using graph paper is not the same as, nor does it replace, using a ruler!) -2011 All Rights Reserved

Also, make sure you draw your axes large enough that your graph will be easily visible. On a standard-sized sheet of paper (8.5 by 11 inches, or A4), you will be able to fit two or three graphs on a page. If you are fitting more than three graphs on one side of a sheet, then you’re probably drawing them too small.  Here are my axes:

Remember that the arrows indicate the direction in which the values are increasing. Your book (and even your teacher) may draw things incorrectly, but that’s no excuse for you. Arrows go on the upper numerical ends of each axis, and NOWHERE ELSE (unless you have an educator who wants it drawn wrong; then just remember the right way for later courses).

Once I’ve drawn my axes, I have to label them with an appropriate scale. “Appropriate” means “one that is neat and that fits the numbers I’m working with”. For instance, considering the values I’m working with, I’ll count off by ones. But if I were doing a graph for a word problem about government waste, I would probably count off by hundred thousand or maybe even by millions. Adjust the scales and axes to suit the case at hand. And ALWAYS use a ruler to make sure that your tick-marks are even!   Here’s my scale:

Note that I’ve made every fifth tick-mark a bit longer. This isn’t a rule, but I’ve often found it helpful for counting off the larger points; it’s more of a time-saver than anything else.

Now I’ll plot (draw) the points I’d computed in my T-chart:

Graph y = (–5/3)x – 2

First I’ll do the chart.

Since I am multiplying x by a fraction, I will x-values that are multiples of 3, so the denominator will cancel out and I will not have fractions. Then I will plot my point and draw my graph.

First I will do the chart Graph y = 7 – 5x

This equation is an example of a situation in which you will probably want to be particular about the x-values you pick. Because the x is multiplied by a relatively large value, the y-values grow quickly. For instance, you probably wouldn’t want to use x = 5 or x = –3. You could pick larger x-values if you wished, but your graph would get awfully tall.

And as you can see, the graph is pretty tall and already.

Form of linear equation

y = mx + c

Another way of arranging the equation y = 4x – 7 is to put the variables in alphabetical order, equating to zero: 4x – y – 7 = 0. This equation is in the form ax + by + c = 0, where the graph y = 4x – 7 is also the graph 0f 4x – y – 7 = 0.

ASSESSMENT

The equations above are all in the form y = mx + c, where x and y are variables and m and c are constants. For example, the equation y = 4x – 7, so m = 4 and c = 7.