Identify equation of a line

Question

Identify the equation of a line in slope-intercept form that’s is perpendicular to y=-1/3x +2 and passes through (2,1)

Answer 1

Important pieces of information to extract: perpendicular to an equation with slope -1/3 and passes through (2,1)

The first piece of information gives us the slope of the line we want. If line a is perpendicular to line b, then the slope of line a is the negative inverse of the slope to line b.

Negative inverse of -1/3 = +3

Now use the point to find the intercept by plugging it in and solving:

y = 3x + b

1 = 3(2) + b

1 = 6 + b

b = 1-6 = -5

Ans: y = 3x-5