Find the equation of the line that is perpendicular to the given line and passes through the given point

Question

Find the equation of the line that is perpendicular to the given line and passes through the given point

y = -1/3x -5; (12,,0)

Answer 1

slope of line perpendicular to y = (-1/3) x - 5 = 3

y = 3x + b

substitute (12,0) for x and y to find b

0 = 36 + b

b = -36

y = 3x - 36

Answer 2

Hello, May,

Mark M. raises a valid question. As written, the equation looks like -1/(3x) - 5.

I'll assume the equation is y = - (1/3)x -5.

Linear equations can be written in the form y - mx + b, where m is the slope and b is the y-intercept, the value of y when x = 0.

A perpendicular line has a slope that is the negative reciprocal of the original slope, -(1/3) in this case. That means a line perpendicular would have a slope of 3, so we can write y - 3x + b. We don't know b yet, but any line with this slope will be perpendicular. The value of b simply shits this line left of right.

We find b by entering the one point we know is on the line, (12,0). Just enter these values of (x,y) into the equation:

12 = 3*0 + b

b = 12

So the line perpendicular to y = -(1/3)x - 5 is y = 3x + 12

Bob