Given:
Slope = 1/3
Contain the point = ( -3,-1 )
Find-:
The equation of a line.
Explanation-:
The general equation of a line is:
[tex]y=mx+c[/tex]
Where,
[tex]\begin{gathered} m=\text{ Slope} \\ \\ c=\text{ y-intercept} \end{gathered}[/tex]
Given the slope is 1/3, then the equation of the line become.
[tex]\begin{gathered} m=\frac{1}{3} \\ \\ y=mx+c \\ \\ y=\frac{1}{3}x+c \end{gathered}[/tex]
The value of y-intercept is:
The point (-3,-1) contains the line so its satisfied the equation.
[tex]\begin{gathered} (x,y)=(-3,-1) \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} y=\frac{1}{3}x+c \\ \\ -1=\frac{1}{3}(-3)+c \\ \\ -1=-1+c \\ \\ c=-1+1 \\ \\ c=0 \end{gathered}[/tex]
So equation of line become:
[tex]\begin{gathered} y=mx+c \\ \\ y=\frac{1}{3}x+0 \\ \\ y=\frac{1}{3}x \\ \\ 3y=x \\ \\ x-3y=0 \end{gathered}[/tex]
The final equation of line is:
[tex]x-3y=0[/tex]
