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Mathematics
Math
Graph the line with the equation y = 3 x 3 y=3x-3.
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To graph the line with the equation y = 3 x 3 y=3x-3, we can use the slope-intercept form of a line where the equation is written as y = m x + b y=mx+b, where m m is the slope, and b b is the y-intercept.
In this case, the slope m = 3 m=3 and the y-intercept b = 3 b=-3, so we can start by plotting the point ( 0 , 3 ) (0,-3) on the y-axis:
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. (0,-3)
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Then, from that point, we can use the slope of 3 to find another point. This means that for every 1 unit we move to the right, we move up by 3 units. So from the point ( 0 , 3 ) (0,-3), we can move right 1 unit and up 3 units to get the point ( 1 , 0 ) (1,0):
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. (1,0)
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We can continue this pattern by moving right 1 unit and up 3 units from the point ( 1 , 0 ) (1,0) to get the point ( 2 , 3 ) (2,3):
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. (2,3)
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We can also move left 1 unit and down 3 units from the point ( 0 , 3 ) (0,-3) to get the point ( 1 , 6 ) (-1,-6):
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. (-1,-6)
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We can continue this pattern as far as we want on both sides of the y-axis:
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. (-2,-9)
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 . (0,-3) ---------------------
 . (2,3)
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. (1,0)
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Finally, we can connect the points with a straight line to get the graph of the line y = 3 x 3 y=3x-3:
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.
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|\\
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\\
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\\
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.*-------------
 .
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\\
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\\
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