Answer :
For 2 lines to be parallel, they have to have the same slope. It means we need to find the slope intercept point form of line q to find the slope of both lines.
[tex]\begin{gathered} 5y-4x=10 \\ 5y=4x+10 \\ y=\frac{4}{5}x+2 \end{gathered}[/tex]Both lines have a slope of 4/5.
Now, use the point slope formula to find the equation of the unknown line.
Remember the point slope formula:
[tex]y-y1=m(x-x1)[/tex]Where m is the slope and x1 and y1 are the coordinates of the given point (-15, 8). Replace these values in the formula:
[tex]\begin{gathered} y-8=\frac{4}{5}(x+15) \\ y-8=\frac{4}{5}x+12 \\ y=\frac{4}{5}x+12+8 \\ y=\frac{4}{5}x+20 \end{gathered}[/tex]This is the slope intercept form of the equation of the unknown line. To convert it to standard form clear the constant term:
[tex]\begin{gathered} y=\frac{4}{5}x+20 \\ 5y=4x+100 \\ 5y-4x=100 \end{gathered}[/tex]That is the equation in standard form of the line parallel to line q that passes through the point at (-15,8).
