Given:
Equation of line:
[tex]2y-3=-2(3-2x)[/tex]
Line pass ( 10,6) and parallel to a given line
Find-:
Equation of another line.
Explanation-:
Given line is:
[tex]\begin{gathered} 2y-3=-2(3-2x) \\ \\ 2y-3=-6+4x \\ \\ 2y=4x-6+3 \\ \\ 2y=4x-3 \\ \\ y=\frac{4x}{2}-\frac{3}{2} \\ \\ y=2x-\frac{3}{2} \end{gathered}[/tex]
Compared with the general form of the equation:
[tex]y=mx+c[/tex]
Where,
[tex]\begin{gathered} m=\text{ Slope} \\ \\ c=y-\text{ intercept} \end{gathered}[/tex]
Then
[tex]\begin{gathered} m=2 \\ \\ c=-\frac{3}{2} \end{gathered}[/tex]
The slope of a line is 2 so the slope of the parallel line is also the same then the equation becomes:
[tex]\begin{gathered} y=mx+c \\ \\ y=2x+c \end{gathered}[/tex]
For the value of "c"
Line pass (10,6) then,
[tex](x,y)=(10,6)[/tex][tex]\begin{gathered} y=2x+c \\ \\ (x,y)=(10,6) \\ \\ 10=2(6)+c \\ \\ 10=12+c \\ \\ c=10-12 \\ \\ c=-2 \end{gathered}[/tex]
So, equation of parallel line is:
[tex]\begin{gathered} y=mx+c \\ \\ y=2x-2 \end{gathered}[/tex]
