Question

What is an equation of the lines that passes through (-9, 12) and is perpendicular to the lines whose equation is y= 1/3x + 6

Answer 1

The equation of the perpendicular line is y=-3x-15.

Step-by-step explanation:

Given the line y=1/3x+6

Comparing it with the slope-intercept form: y=mx+b

`\text{Slope}=(1)/(3)`

Let the slope of the perpendicular line = m

Two lines are perpendicular if the product of their slopes is -1.

Therefore:

`\begin{gathered} (1)/(3)m=-1 \\ m=-3 \end{gathered}`

To find the equation of the perpendicular line passing through (-9, 12), we use the point-slope form.

`y-y_1=m(x-x_1)`

Substituting the slope and point (-9,12), we have:

`\begin{gathered} y-12=-3(x-(-9)) \\ y-12=-3(x+9) \\ y-12=-3x-27 \\ y=-3x-27+12 \\ y=-3x-15 \end{gathered}`

The equation of the perpendicular line is y=-3x-15.