Is line 1 parallel to line 2? Briefly explain your answer. Line 1 3x + 2y = 8 Line 2 y = 2/3 x + 9?

Question

do I have to solve for x and y in the first line? Please explain to me the formula in which I have to use to solve this.

GREAT HELP EVERYONE!! :o) I completely understand the formula now. Thank you sooo very much! I will pick the best answer tomorrow...i wish i could pick all of you

:p

Answer 1

Line 1
2 y = - 3 x + 8
y = (- 3 / 2) x + 4
m1 = (- 3 / 2)

Line 2
y = (2 / 3) x + 9
m2 = (2 / 3)

m1 ≠ m2 so lines are not parallel.

Answer 2

if two lines are parallel, then they have the same slope. however, if the slope to Line 2 is a negative reciprocal of the slope of Line 1, then the two lines are perpendicular.

i.e. from the general equation:

y=mx+c, if "m" for both equation is the same, then they are parallel, so:

Line 1:
3x+2y=8
y=4-3/2x ------ here m = -3/2

Line 2:
y=2/3x + 9 ------- here m = 2/3

therefore, since "m" for both lines is different, you can safely conclude that these two lines are NOT parallel. however, since "m" for Line two IS the negative reciprocal of Line 1, you can safely conclude that the two lines are perpendicular.

to show the perpendicularity of the lines, we calculate negative reciprocals as follows:

lets work with Line 1, m1=-3/2
to get the -ve reciprocal, you do m2 = -(1/m1)
m2=-(1/(-3/2)) = 1/(3/2) = 1 x (2/3) = 2/3

SO:
since both lines don't have the same slope, they are NOT parallel

HOWEVER:
since the slope for Line 2 is a negative reciprocal of the slope for Line 1, the two lines ARE perpendicular

Answer 3

Put the two lines in the form of y=ax+b

If both lines have the same value for a then they are parallel (as they have the same gradient)

Line 1) 3x+2y =8 => 2y=-3x +8 => y=(-3/2)x - +4

Line 2) y=2/3 x + 9

Lines are NOT parallel. In fact - lines are perpendicular since gradient for line 1 = -1/gradient for line 2

Answer 4

3x+2y=8

2y=8-3x

y=4-1.5x

y=-1.5x+4

that's line 1

line 2 is

y=2/3x+9

they are not parallel because 2/3 does not equal -1.5. those are the slopes, which must be equal for the lines to be parallel. however, before you can compare slopes, you have to rearrange the equation so that it is in the form y=mx+b. in the case of line 2, 9=b and 2/3=m, the slope of the line.

Answer 5

No, they are not parallel.
To be parallel, the slopes have to be the same.
So first set the equation to fit the formula y=mx +b
So for the first equation, solve for y. You end up with y= (-3/2)x +4
and the second keep it as it is.
The slope, m, needs to be the same. In this case they are not, so they are not parallel.

Answer 6

Hi,

Putting each equation in point-intercept form, we have

y = -(3 / 2)·x + 4

and

y = (1 / 3)·x + 9 / 2

By virtue of the fact that the two lines lie in the same plane, and their slopes are different ( -3 / 2 ≠ 1 / 3), the two lines are not parallel.

James :-)

Answer 7

You have to solve for y, so it is in y = mx + b form. If they are parallel then they both have the same m(slope)

3x + 2y = 8
2y = -3x + 8
y = -3/2x + 4

They are not parallel they are actually perpendicular because their slopes are negative reciprocals.