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Question 1116981: Given the lines 3x-2y-24=0 and 4x+7y=-26
Find the point on the y axis that is collinear with P(4,-6), if the line has a gradient of 2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! it appears that what you are looking for is the equation of the line that has a slope of 2 that goes through the point (4,-6).
the slope intercept form of the equation of a line is y = mx + b
m is the slope and b is the y-intercept.
the slope is 2, therefore the equation becomes y = 2x + b.
to find b, replace x and y with the value of one of the points on the line and solve for b.
your equation becomes -6 = 2*4 + b
solve for b to get b = -6 - 8 = -14.
the y-intercept is the value of y when x is equal to 0.
that's the point where the line that is co-linear with (4,-6) meets the y-axis if the line has a gradient of 2 (gradient = slope).
your point is therefore (0,-14).
in my view, the other two equations are superfluous to the problem.
as it turns out, however, ths point (4,-6) is the intersection of the line formed by those equations.
the following graph shows you what i mean.
the line with the gradient of 2 is the green line.
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