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Step-by-step explanation:
I'll assume these are the equations:
11x + y = 18
4x + y = 18
-2x - 2y = 18
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The easiest approach to graphing, for me, is to rearrange each to y=mx+b (slope-intercept) format:
- y = -11x+18 y-intercept of 18 (0,18)
- y = -4x + 18 y-intercept of 18 (0,18)
- y = - x -9 y-intercept of -9 (0,-9)
It seems to me that all three can be graphed easily from simply reading the slope and y-intercept values. Since these are straight lines, all we need is two points for each line, and one is standing out in plain view, the y-intercept: (0,y-intercept). The second point can be determined by using whatever value of x makes the calculation easy
An example: y = - x -9. Plot (0,-9) for the y intercept, and then calculate one additional point (e.g., for x = - 9). (-9,0) Then connect a straight line between these two points and presto (metric term for magic), a graph. For the first equation, I picked 20 for x. For x = 20, y = -29. That was easy, and we have the second point: (1,-10)
See the attachment for how this was done. The first points are all for the y-intercept (0,[18 or 9]). All of the second points were calculated in my head by using a convenient value for x.
This approach doesn't work well for non-linear equations. There, I find it easier to set up a table of values - a spreadsheet such as Excel is my tool for the calculations.
The attachment also demonstrates the Really Easy Way to graph functions. DESMOS, a free, and excellent, online calculator.
