Question

write an equation of the lien containing th given point and parallel to the given line (-4,4) 9x=4y+3

Answer 1

parallel lines have the same slope.
lets rewrite the given equation in the slope intercept form.
do that and post what you get.

Answer 2

Parallel lines have the same slope, so the slope of the parallel line can be determined from the equation you are given.

slope = 9/4

y = (9/4)x + instercept

substitute the point (-4,4) in this equation (y = (9/4)x + instercept) to determine the value of the intercept.

slope = \cfrac{9}{4}
4 = \left(\cfrac{9}{4}\right)\left(-4\right)+intercept

The solution is attached.

Answer 3

Oops... getting the hang of the type setting...I meant:

\[slope = \cfrac{9}{4}\]
\[4 = \left(\cfrac{9}{4}\right)\left(-4\right)+intercept\]

Answer 4

Parallel lines have the same coefficients of x and y, constant term is different.
The equation of the line containing the given point and parallel to the given line (-4,4) 9x=4y+3 will be
9x = 4y +c
Plug in x =-4, y =4 and solve for c
9*(-4) = 4*4 +c
-36 = 16 + c
-52 =c
Equation of line is 9x = 4y -52