FINDING THE PERPENDICULAR EQUATION

Question

through (4,2) and perpendicular to y=-3/4x-5

What’s the equation of the line in standard form?

Answer 1

Greetings! Lets solve this shall we!?

We are looking for the line perpendicular to the given line y = (-3/4)x - 5, right ?

First, when we have to find the line perpendicular to the given line, we must reciprocate the slope such that

m = (-3/4) changes into -(-4/3) = 4/3. Then, we pull out the point-slope formula to finish finding the perpendicular. So, adding in the slope 4/3 and point (4,2) for (x1,y1) we get,

y - y₁ = m ( x - x₁)

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

y - 2 = (4/3)x - (16/3)

y = (4/3)x - (16/3) + 2

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

Finally the standard form of the equation is -(4/3)x + y = (-10/3)

I hope this helped!