Question

The equation of line cis y = -6x - 3. Line d includes the point (3, -3) and is perpendicular to

line c. What is the equation of line d?

Answer 1

Given:

The equation of line c is,

`y=-6x-3`

Line d is perpendicular to line c, that means their slopes will be opposite reciprocals.

Slope of line c is,

`\begin{gathered} \text{For y=mx+c} \\ m=\text{ slope} \\ y=-6x-3 \\ \text{slope =m}_1=-6 \end{gathered}`

It gives,

`\begin{gathered} m_1* m_2=-1 \\ -6* m_2=-1_{} \\ m_2=-(1)/(-6)=(1)/(6) \end{gathered}`

So, slope of the line d is 1/6.

Also line d includes point ( 3, -3 )

The point slope form of equation of line is,

`\begin{gathered} y-y_1=m_2(x-x_1) \\ (x_1,y_1)=(3,-3) \\ y-(-3)=(1)/(6)(x-3) \\ y+3=(1)/(6)x-(3)/(6) \\ y=(1)/(6)x-(1)/(2)-3 \\ y=(1)/(6)x-(7)/(2) \end{gathered}`

Answer: the equation of line d is,

`y=(1)/(6)x-(7)/(2)`