Answer:
Parallel
Step-by-step explanation:
Instead of putting this and slope intercept form. I'm going determine the
x-intercept and the y-intercept of both.
The x-intercept can be found by setting y to 0 and solving for x.
The y-intercept can be found by setting x to 0 and solving for y.
So let's look at 3x-2y=5.
x-intercept?
Set y=0.
3x-2(0)=5
3x =5
x =5/3
y=intercept?
Set x=0.
3(0)-2y=5
-2y=5
y=-5/2
So we are going to graph (5/3,0) and (0,-5/2) and connect it with a straightedge.
Now for 6y-9x=6.
x-intercept?
Set y=0.
6(0)-9x=6
-9x=6
x=-6/9
x=-2/3
y-intercept?
Set x=0.
6y-9(0)=6
6y =6
y =1
So we are going to graph (-2/3,0) and (0,1) and connect it what a straightedge.
After graphing the lines by hand you can actually do an algebraic check to see if they are parallel (same slopes), perpendicular (opposite reciprocal slopes), or neither.
Let's find the slope by lining up the points and subtracting then putting 2nd difference over 1st difference.
So the points on line 1 are: (5/3,0) and (0,-5/2)
(5/3 , 0 )
- (0 ,-5/2)
-----------------
5/3 5/2
The slope is (5/2)/(5/3)=(5/2)*(3/5)=3/2.
The points on line 2 are: (-2/3,0) and (0,1)
(-2/3 , 0)
- ( 0 , 1)
-----------------
-2/3 -1
The slope is -1/(-2/3)=-1*(-3/2)=3/2.
The slopes are the same so they are parallel. The line lines are definitely not the same; if you multiply the top equation by -3 you get -9x+6y=-15 which means the equations are not the same. Also they had different x- and y-intercepts. So these lines are parallel.
This is what we should see in our picture too.
