The general equation of a line in slope-intercept form is given by:
[tex]y=mx+c[/tex]Given the equation of a line to be
[tex]y=2x+5[/tex]Upon comparing the equation to the general line equation, then
[tex]\begin{gathered} m=2 \\ c=5 \end{gathered}[/tex]Next, to find the equation of the line parallel to the given line
we will use the formula
[tex]y-y_1=m(x-x_1)[/tex]where
[tex]\begin{gathered} m=2 \\ x_1=2 \\ y_1=-4 \end{gathered}[/tex][tex]\begin{gathered} y-(-4)=2(x-2) \\ y+4=2x-4 \\ y=2x-4-4 \\ y=2x-8 \end{gathered}[/tex]The equation of the line is y=2x -8
