Find the equation for the line perpendicular to 2x -5y = 20 that passes through the point (-1/2,4). Answer should be in y = mx + b form.
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We will first identify the slope of the given line, we can do that by rewriting it into the form y = mx + b.
Subtract both sides of the equation by 2x.
-5y = -2x + 20
Divide both sides by -5.
y = 2/5x - 4
So, slope = 2/5.
Since, the equation we are finding is perpendicular to the given point the slope of it is negative reciprocal of 2/5.
So slope of our line is -5/2.
We now have slope = -5/2 and a point (-1/2, 4).
Using the point-slope form:
y - (-1/2) = -5/2(x - 4)
y + 1/2 = -5/2x + 20/2
y + 1/2 = -5/2x + 10
Subtract 1/2 on both sides.
y = -5/2x + 10 - 1/2
y = -5/2x + 20/2 - 1/2
Hence, our line is y = -5/2x + 19/2.
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