Question

What is the equation of a line passes thru the point (4, 2) and is perpendicular to the line whose equation is y = ×/3 - 1 ??

Answer 1

y = -3x + 14

Explanation:

First find the reciprocal slope since it is perpendicular. Slope of the other line is 1/3 so the slope for our new equation is -3.

Plug information into point-slope equation

(y - y1) = m (x-x1)

y - 2 = -3 (x-4)

Simplify if needed

y - 2 = -3x + 12

y = -3x + 14

Answer 2

Perpendicular lines have slopes that are opposite and reciprocal. Therefore, the line we are looking for has a -3 slope.

y= -3x+b

Now, we can substitute in the point given to find the intercept.

2= -3(4)+b

2= -12+b

b=14

Finally, put in everything we've found to finish the equation.

y= -3x+14