What is the equation of the line in slope-intercept form that is perpendicular to the line y =3/4 x – 2 and passes through the point (–12, 10)?

Slope intercept form : y=mx+b , where m=slope, y=y-intercept

Perpendicular to : y = 3/4x - 2 ; Passes through (-12, 10)

**Remember : When finding the slope of a perpendicular line, we must get the negative reciprocal **

Ex of negative reciprocal : 3/2 → -2/3

The original line has a slope of 3/4, therefore our perpendicular slope is -4/3

Now we have to use the point-slope formula to find our new equation.

y - y₁ = m(x - x₁)

Passes through (-12, 10) ; slope = -4/3

y₁ = 10 ; x₁ = -12

Simply plug in the numerals for y₁ and x₁ as well as m.

y - (10) = -4/3(x - (-12))

Simplify.

y - 10 = -4/3(x + 12)

Simplify.

y - 10 = -4/3x - 48/3

Simplify -48/3

-48/3 = -16

y - 10 = -4/3 - 16

Now, we need to put this into slope-intercept form.

**Remember : slope intercept form is y=mx+b where m=slope, y=y-intercept**

So, add 10 to both sides.

y = -4/3x - 16 + 10

Simplify.

y = -4/3x - 6

~hope I helped!~

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step-by-step explanation:

step-by-step explanation: