Given:
Line pass through ( 3, 4)
Parallel to the,
[tex]y=-\frac{2}{3}x+1[/tex]
Find-:
The equation of a line.
Explanation-:
The slope of the parallel line is also the same.
[tex]m_1=m_2[/tex]
Where
m is the slope of a parallel line
The general equation of a line is:
[tex]y=mx+c[/tex]
So the equation become is:
[tex]\begin{gathered} y=mx+c \\ \\ y=-\frac{2}{3}x+c \end{gathered}[/tex]
The line pass ( 3,4)
That mean,
[tex](x,y)=(3,4)[/tex][tex]\begin{gathered} y=-\frac{2}{3}x+c \\ \\ (x,y)=(3,4) \\ \\ 4=-\frac{2}{3}(3)+c \\ \\ 4=-2+c \\ \\ c=4+2 \\ \\ c=6 \end{gathered}[/tex]
So the equation of a line is:
[tex]\begin{gathered} y=-\frac{2}{3}x+6 \\ \\ y=\frac{-2x}{3}+\frac{18}{3} \\ \\ y=\frac{-2x+18}{3} \\ \\ 3y=-2x+18 \\ \\ 2x+3y=18 \end{gathered}[/tex]
