The line goes through (0,2) and (2,-1). See the graph below.
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Explanation:
The given equation is in the form y = mx+b
m = -3/2 is the slope
b = 2 is the y intercept
The y intercept tells us where the graph crosses the vertical y axis. In this case, it's at 2 on the y axis. Think of the y axis as a number line that is simply vertical.
So we'll have (0,2) as one point on the line.
From this point, move down 3 units and to the right 2 units to arrive at (2,-1) as our next point. We only need two points to graph a straight line. You can repeat the process "down 3, over to the right 2" to generate as many points as you want.
The "down 3, over to the right 2" is from the slope -3/2
slope = rise/run = -3/2
rise = -3 means we move down 3
run = 2 means we move to the right 2
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Another approach is to plug in numbers for x to get corresponding values for y.
If we pick on x = 0, then,
y = (-3/2)*x + 2
y = (-3/2)*0 + 2
y = -1.5*0 + 2
y = 0 + 2
y = 2
So this shows (0,2) is one point on the line.
If we plug in x = 2, then,
y = (-3/2)*x + 2
y = (-3/2)*2 + 2
y = -1.5*2 + 2
y = -3+2
y = -1
Meaning (2,-1) is another point on the line.
