Respuesta :
In order to be parallel, the lines have to have the same slope.
When we have lines expressed in the form:
[tex]ax+by=C[/tex]the slope has the value of the quotient:
[tex]m=\frac{-a}{b}[/tex]Then, if both lines have the same value for this quotient, both lines ahve the same slope. Therefore, they are parallel.
In our case, the slope of the parallel line is:
[tex]m=\frac{-a}{b}=\frac{-5}{2}=-2.5[/tex]We will start by using the same values for a and b for our line. So a=5 and b=2.
Our line has to go through the point (-8,20).
We can use it to calculate C, in order to make the line go through this point.
We replace our equation with coordinates of the point and solve it for C:
[tex]\begin{gathered} ax+by=C \\ 5x+2y=C \\ 5(-8)+2(20)=C \\ -40+40=C \\ C=0 \end{gathered}[/tex]The equation of the line in the form ax + by = c, passing through ( -8,20) and parallel to 5x + 2y = 11 is 5x+2y=0
