Respuesta :
The slope intercept form of a line is given by:
[tex]\begin{gathered} y=mx+b \\ where \\ m=slope \\ b=y-intercept \end{gathered}[/tex]Two lines are parallel if:
[tex]m1=m2[/tex]Where:
m1 = slope of the line 1
m2 = slope of the line 2
Rewrite the equations in the slope intercept form:
[tex]\begin{gathered} y-3x=4 \\ y=3x+4 \end{gathered}[/tex]From the previous equation we can conclude that the slope is m = 3, since the line we need to find is parallel to this one, we can conclude that the slope of the line we are trying to find is also m = 3
For the other equation:
[tex]\begin{gathered} 4y+x=36 \\ 4y=36-x \\ y=-\frac{1}{4}x+9 \end{gathered}[/tex]From this line we can conclude that the y-intercept is b = 9, since the line we are trying to find has the same y-intercept, we can conclude that its y-intercept is also b = 9. Therefore, the equation of the line is:
[tex]y=3x+9[/tex]