Answer :
Answer:
[tex]\large\boxed{y=\dfrac{7}{2}x-18}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
Convert the equation of a line 3x + 4x = 2y - 9 to the slope-intercept form:
[tex]3x+4x=2y-9[/tex]
[tex]7x=2y-9[/tex] add 9 to both sides
[tex]7x+9=2y[/tex] divide both sides by 2
[tex]\dfrac{7}{2}x+\dfrac{9}{2}=y\to y=\dfrac{7}{2}x+\dfrac{9}{2}[/tex]
Parallel lines have the same slope. Therefore we have the equation:
[tex]y=\dfrac{7}{2}x+b[/tex]
Put the coordinates of the point (4, -4) to the equation:
[tex]-4=\dfrac{7}{2}(4)+b[/tex]
[tex]-4=7(2)+b[/tex]
[tex]-4=14+b[/tex] subtract 14 from both sides
[tex]-18=b\to b=-18[/tex]
Finally we have the equation:
[tex]y=\dfrac{7}{2}x-18[/tex]