Find an equation of the line passing through point (4, - 5) and perpendicular to the line whose equation is 3x - 6y = - 11

Answer 1

When you multiply the slopes of perpendicular lines the product is always -1. Therefore, we must first find the slope of the given line. To do this we need to put the equation given into the form of y=mx+b, where m is the slope and b is the y-intercept.

3x-6y=-11 original equation

3x=-11+6y add 6y to both sides

3x+11=6y add 11 to both sides to isolate the "y" term

6y=3x+11 rearrange

y=(3x/6)+(11/6) divide both sides by 6

y=(1/2)x+(11/6) simplify

From here we can see that the slope of the original line is 1/2. The slope of the new line has to be the negative inverse of this in order to make the products of the slopes equal to -1. Therefore, the slope of the new line is -2. Using this for m and the point (4,-5) for x and y, we can solve for b:

y=mx+b

-5=(-2)(4)+b

-5=-8+b

b=8-5

b=3

With m = -2 and b = 3, we now get for y=mx+b--->y=-2x+3

Hope this helps!