Answer:
Let's put this equation in standard form...
[tex]2x+4y=56\\4y=56-2x\\y=14-0.5x[/tex]
If it is parallel, it would have the SAME slope but ANY OTHER y-intercept!!
For example...
[tex]y=-0.5x+304\\y=-0.5x-67[/tex]
Hope this helps!!
Hi there !
Lets first try to write given line in slope intercept form which is -
❄︎[tex]\green{ \underline { \boxed{ \sf{y=mx+c}}}}[/tex]
Here-
Proceeding-
✰2x + 4y = 56
➪ 4y = -2x +56
➪ y =[tex]\dfrac{ -2x +56}{4}[/tex]
➪ y =[tex]\dfrac{ -2x }{4}+ \dfrac{56}{4}[/tex]
➪ y =[tex]\dfrac{ -x }{2}+ 14[/tex]
➪ y =[tex]\dfrac{ -1}{2}x + 14[/tex]
Comparing with slope intercept form -
❄︎[tex]\red{ \underline { \boxed{ \sf{m = - \frac{1}{2}}}}}[/tex]
Now,
✪ Since the parallel lines have same inclination with positive x-axis , their slopes are equal.
❀ So, the slope of a line parallel to the line whose equation is 2x + 4y = 56 would be [tex]-\dfrac{1}{2}[/tex]
