Question

write an equation in slope intercept form for the line that passes through (4, -4) and is parallel to 3x+4x=2y-9

Answer 1

Answer:

$\large\boxed{y=\dfrac{7}{2}x-18}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

Convert the equation of a line 3x + 4x = 2y - 9 to the slope-intercept form:

$3x+4x=2y-9$

$7x=2y-9$             add 9 to both sides

$7x+9=2y$       divide both sides by 2

$\dfrac{7}{2}x+\dfrac{9}{2}=y\to y=\dfrac{7}{2}x+\dfrac{9}{2}$

Parallel lines have the same slope. Therefore we have the equation:

$y=\dfrac{7}{2}x+b$

Put the coordinates of the point (4, -4) to the equation:

$-4=\dfrac{7}{2}(4)+b$

$-4=7(2)+b$

$-4=14+b$       subtract 14 from both sides

$-18=b\to b=-18$

Finally we have the equation:

$y=\dfrac{7}{2}x-18$