Question

A line contains the point ( -3, -1 ) and has a slope of 1/3. which equation represents this line?

Answer 1

Given:

Slope = 1/3

Contain the point = ( -3,-1 )

Find-:

The equation of a line.

Explanation-:

The general equation of a line is:

`y=mx+c`

Where,

`\begin{gathered} m=\text{ Slope} \\ \\ c=\text{ y-intercept} \end{gathered}`

Given the slope is 1/3, then the equation of the line become.

`\begin{gathered} m=(1)/(3) \\ \\ y=mx+c \\ \\ y=(1)/(3)x+c \end{gathered}`

The value of y-intercept is:

The point (-3,-1) contains the line so its satisfied the equation.

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

`\begin{gathered} y=(1)/(3)x+c \\ \\ -1=(1)/(3)(-3)+c \\ \\ -1=-1+c \\ \\ c=-1+1 \\ \\ c=0 \end{gathered}`

So equation of line become:

`\begin{gathered} y=mx+c \\ \\ y=(1)/(3)x+0 \\ \\ y=(1)/(3)x \\ \\ 3y=x \\ \\ x-3y=0 \end{gathered}`

The final equation of line is:

`x-3y=0`