Answer: Plot the two points (0,0) and (1,3). Draw a straight line through them. The graph is shown below.
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Explanation:
When x = 0, we have y equal to...
y = 3x
y = 3*0
y = 0
So this means (x,y) = (0,0) is one point on the line
Let's follow those steps for x = 1
y = 3x
y = 3*1
y = 3
So the point (x,y) = (1,3) is also on the line.
You can repeat this process for any x value you want; however, we only need two points to form the line. Plot (0,0) and (1,3). Then draw a straight line through both points. Extend the line as far as you can in either direction. This forms the graph of y = 3x.
You can use a graphing calculator (eg: TI83) to get the job done. Or you can use a free online resource such as GeoGebra or Desmos. I prefer GeoGebra as it offers more options. The graph shown below was made with GeoGebra.
Note that moving from point A(0,0) to B(1,3) has us move up 3 and over to the right 1. This is due to the slope of 3 = 3/1.
y = 3x is the same as y = 3x+0. It is of the form y = mx+b with m = 3 = 3/1 as the slope and b = 0 as the y intercept.
