Question

Use the information given to find the equation of the line using the point-slope formula (y-y_1)=m(x-x_1)). Then convert your answer to slope-intercept form (y=mx+b).perpendicular to 3y=x-4 and passes through the point (−2,1).To earn full credit be sure to clearly identify your point slope equation and your slope intercept equation. Include all steps and calculations.

Answer 1

The product of the slopes of the perpendicular line is -1, which means if the slope of one of them is m, then the slope of the other is -1/m (reciprocal the value and change the sign)

Since the equation of the given line is

`3y=x-4`

Divide both sides by 3 to put the equation in the form y = mx + b, m is the slope

`\begin{gathered} (3y)/(3)=(x)/(3)-(4)/(3) \\ y=(1)/(3)x-(4)/(3) \end{gathered}`

Then the slope of the given line is 1/3

To find the slope of the perpendicular line reciprocal 1/3 and change its sign

Then the slope of the perpendicular line is -3

The point-slope form is

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

Since m = -3, x1 = -2, y1 = 1, substitute them in the given form

`\begin{gathered} y-1=-3(x-\lbrack-2\rbrack) \\ y-1=-3(x+2) \end{gathered}`

The point-slope form of the equation of the perpendicular line is

`y-1=-3(x+2)`

To change it to the form of y = mx + b, simplify the right side

`\begin{gathered} y-1=-3(x)-3(2) \\ y-1=-3x-6 \end{gathered}`

Add 1 to both sides

`\begin{gathered} y-1+1=-3x-6+1 \\ y=-3x-5 \end{gathered}`

The slope-intercept equation of the perpendicular line is

`y=-3x-5`