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

Question

im trying to figure it out but i forget the steps

Answer 1

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