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in slope intercept form how would you find perpendicular line to y=3/4x+1 and goes through the point (9,-2)

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1 Answer

the slope of the line with the equation y = (3/4)x + 1 is 3/4

any line perpendicular to the given line has a slope -1/(3/4) which is equivalent to -4/3

now we know the slope of the perpendicular line

now we use the point slope form to figure out the equation of the perpendicular line:

y - y1 = m * ( x - x1)        eq. 1

we know: x1 = 9, y1 = -2, and m is the slope of the perpendicular line (which is -4/3); plug in these values to eq. 1;

y - (-2) = (-4/3) * (x - 9)

y + 2 = (-4/3)x + 12

now, we have to put the above equation in the form:  y = mx + b, which is the slope intercept form.

y = (-4/3)x + 12 - 2

y = (-4/3)x + 10