The line is paralle to -3x+2y=9 and contain the point (-2,1)?

Answer 1

The line will have the same slope as the one
given, since the two are parallel, and the problem gives one point. Sounds like a case for the Point-Slope canonical form:

y - y1 = m(x - x1)

Just need the slope of the given line, and the
Slope-Intercept form y = mx + b should give that:

-3x+2y = 9

2y = 3x+9

y = (3/2)x+9/2 ==> slope, m=3/2

Now, substituting into Point-Slope form,

y - 1 = (3/2)(x - (-2))

y = (3/2)(x + 2) + 1

y = (3/2)x + (3/2)*2 + 1

y = (3/2)x + 3 + 1

y = (3/2)x + 4

Answer 2

2y=3x+9 Y= 3/2x+3 (-2)3/2+z =1 -3+z=1 z=4 so the line parallel to -3x+2y=9 is 3/2x+4=y

Answer 3

parallel lines have the same slope, so the new line starts out
-3x + 2y = .....
just like the old one. To fill in the ...., plug in the point:

-3(-2) + 2(1) = 6+2 = 8,
so the parallel line is
-3x + 2y = 8

Answer 4

-3x + 2y = 9 in slope-intercept form is:

y = (3/2)x + (9/2)

All lines parallel to it will have slope 3/2. Or just use your original form. PLug the point in either and solve for the constant.

1 = (3/2)(-2) + b

b = 4

y = (3/2)x + 4

or

-3(-2) +2(1) = c

The latter is easier. c = 8

-3x + 2y = 8

Answer 5

ok so first you need to find the slope of the line -3x+2y=9

you can do this by putting it into slope intercept form (y=mx+b) where m represents the slope. it will look like this ... y=-3/2x+9/2

once you have the slope of this line (-3/2) you know the slope of the other line, because they have the same slope... thats what parallel means. now you can use the point slope formuka to find the equation of the second line. y - y1=m(x-x1)

so you have y+2= - 3/2 (x-1)
simplify and you have your answer

y= -3/2x -1/2

Answer 6

since the slope is the same for lines that are parallel, you slope for it will be 3/2 ( y=3/2x+9, after necessary algebra done)

the equation of a line is y = mx + b and since you already know the slope, 3/2, and your point (-2,1), you can plug those into the equation and solve for your y intercept, b.

1 = (3/2)(-2) + b
1 = (-3) + b
b = 4

therefore: y = 3/2x + 4