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Question 277282: how do i do a problem like this -16x+2y=-6 through point (16,8)
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! First, get the equation into slope-intercept form: y = mx+b
-16x + 2y = -6
2y = 16x - 6
y = 8x - 3
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But this line does NOT go through the point (16,8), as we can see on a graph.
In fact, y = 125 when x=16.
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However, the general equation y = mx+b can be shifted with any constant 'b'.
8 = 8(16) + b
8 = 128 + b
b = -120
We can graph this as follows.
So the equation y = 8x - 120 will have slope = 8 and it will go through the point (16,8).
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We can check this answer by remembering the slope = rise / run = change in y / change in x.
The slope m = 8.
So if we move one point on the x-axis, there will be a change of 8 on the y-axis.
Given (16,8), we can predict that (15,0) will be on the line. (-1 on the x-axis leads to -8 on the y-axis)
And we can predict (17,16) will be on the line. (+1 on the x-axis leads to +8 on the y-axis)
Looking back at the second graph, we see that is the case.
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