475,711 views
3 votes
3 votes
A line perpendicular to f(x) = 3x + 4 and passing through the

point (3,1)

What’s the slope and the equation of the?

User Benibur
by
2.9k points

1 Answer

7 votes
7 votes

Answer:

y = -(1/3)x + 2

Explanation:

A perpendicular line has a slope that is the negative inverse of the reference line. For a line with slope of 3, the perpendicular line would have a slope of -(1/3). That brings us to an equation of the slope-intercept form of:

y = -(1/3)x + b

Any equation having this form will be perpendicular to y = 3x + 4.

We could pick any value for b and the line will be perpendicular. The b value will only shift the graph up or down, not change the slope. But we are told that this line must go through point (3,1), so we need to pick a value of b that will make this happen.

To do this, enter the point (3,1) into the equation and solve for b:

y = -(1/3)x + b

1 = -(1/3)*3 + b

1 = -1 + b

b = 2

The equation of a line perpendicular to y = 3x + 4 that goes through point (3,1) is:

y = -(1/3)x + 2

See attached image.

A line perpendicular to f(x) = 3x + 4 and passing through the point (3,1) What’s the-example-1
User Alex Coroza
by
3.0k points