Question 248027
The slope-intercept formula is:  y = mx+b.
The slope = m = change in y divided by change x.
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We have an equation y = 2x -3.
m = 2 = slope
It means that for every change in y = 2, there is a change in x = 1.
This extends indefinitely in both directions.  change in y = 4, means change  in x = 2.
Etc.
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The y-intercept = -3, so the related point is (0, -3)
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Adding 4 to y means we add 2 to x, which produces the point (2, 1).
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Plot these two points and draw the line connecting them.
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{{{graph(500,500,-10,10,-10,10,2x-3)}}}
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The same logic applies to the second equation.
y = 2/3x - 4.
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When x =0, y = -4, so we have the point (0, -4)
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The slope = 2/3, which means for every change of 2 in y, there is a change of 3 in x.
So we can use this information to calculate a second point.
Add 2 to y and add 3 to x:  (3, -2)
Plot these point and draw a line.
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{{{graph(500,500,-10,10,-10,10,2/3*x -4)}}}
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You can plot both on the same graph to check if they intercept one another.
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{{{graph(500,500,-10,10,-10,10,2*x-3,2/3*x -4)}}}