Question

A line is perpendicular to y = -⅓x + 1 and intersects the point (-5, 1). What is the equation of this perpendicular line?

Answer 1

Hello :)

Answer -

y = 3x + 16

Step-by-step explanation -

Our task is to find the equation of the line that's perpendicular to y = -⅓x + 1 and intersects the point (-5, 1).

If two lines are perpendicular, their slopes are negative inverses.

The negative inverse of negative one-third is 3.

Now we can find our equation. We will start off by writing the equation in point-slope, and in the end, we will convert to slope-intercept. So here we go:

`\begin{gathered}\sf{y-y_1=m(x-x_1)}\\\sf{{y-1=3(x-(-5)}\\\sf{y-1=3(x+5)}\\\sf{y-1=3x+15}\\\sf{y=3x+15+1}\\\sf{y=3x+16}\end{gathered}`

Answer 2

y = 3x + 16

Explanation:

Remember: Perpendicular lines have the opposite reciprocal slope.

y = -⅓x + 1

the slope of this equation is -⅓. The opposite reciprocal is 3.

y = 3x + b, we don't know what b is. Let's plug in (-5, 1)

1 = 3(-5) + b

1 = -15 + b

b = 16

Therefore, the equation of the line perpendicular to y = -⅓x + 1 and intersects the point (-5, 1) is

y = 3x + 16