Concept: We were told that the point (1,1) is parallel to y = -3x - 1
Let us obtain our slope from the equation given
The general form of equation of line is written in the form
[tex]\begin{gathered} y=mx+c \\ \\ where,m=slope \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} y=-3x-1 \\ \therefore m=-3 \end{gathered}[/tex]
Since, the point is parallel to the line given. Therefore, the slope is the same.
The formula for the equation of the line given one point is,
[tex]y-y_1=m(x-x_1)[/tex]
Thus
[tex]\begin{gathered} y-1=-3(x-1) \\ y-1=-3x+3 \\ y=-3x+3+1 \\ y=-3x+4 \end{gathered}[/tex]
Hence, the equation in its standard form is
[tex]\begin{gathered} 3x+y=4 \\ \end{gathered}[/tex]
