what type of lines are these?

@khan post #17 > You can solve for the point of intersection from the equations of the lines.

here is my work,
At the intersection point, the x value and the y value are equal to each other for both equations.
so i'm going to solve for y in this equation,
3x+2y=-16
3x-3x+2y=-16-3x
2y=-16-3x ( rearranging terms)
2y=-3x-16
1/2(2y) = 1/2( -3x-16)
y=-3/2x-8 this is the value of y
now if i want to set this equal to the other equation, -2x + 3y=12 cos my two y values have to be the same for both equations
so i'm going to plug this equation y=-3/2x-8 into the other one.
please, confirm this for me when you have time before i can continue to plug this value of y into the other equation.
 
eddy2017 said:
@khan post #17 > You can solve for the point of intersection from the equations of the lines.

here is my work,
At the intersection point, the x value and the y value are equal to each other for both equations.
so i'm going to solve for y in this equation,
3x+2y=-16
3x-3x+2y=-16-3x
2y=-16-3x ( rearranging terms)
2y=-3x-16
1/2(2y) = 1/2( -3x-16)
y=-3/2x-8 this is the value of y
now if i want to set this equal to the other equation, -2x + 3y=12 cos my two y values have to be the same for both equations
so i'm going to plug this equation y=-3/2x-8 into the other one.
please, confirm this for me when you have time before i can continue to plug this value of y into the other equation.
Click to expand...
Yes.

You should really try it instead of asking for confirmation. You can always check "correctness" of your result by using those (x,y) values back into the original equations and check if you get back identity (JeffM has shown that to you in previous post).
 
well, now the two y values are the same and i'm gonna find out if the x values are the same too. i like the way Dr Khan put it, checking if i get back identity
so,
-2x +3y=12
let's plug in the value for y
-2x +3(-3/2x-8)=12 ( using the distributive property)
-2x + -9/2x-24=12
(-2x -9/2x)+ -24=12
-5/2x -24 =12 (Adding 24 to both sides)
-5/2x=36 multiplying both sied by the multiplicative inverse
2/-5(-5/2x)=2/-5 * 36
x=-72/5

this is the value of x when y=-3/2x-8 in one equation
i'm pluggin' the same value for y into the other
3x+2y=-16
3x+2(-3/2x-8)=-16
and to make it short the result is
-16+16=-16+16
0=0

i do not see identity here.
 
Jomo said:
So two parallel can't intersect? Sorry, but I will never give into this statement.
Click to expand...


It's "never give in to." Parallel lines (in the plane) are lines that are the same distance apart, and they do not meet. They do not intersect.
 
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i did the work again.
i manipulated both equations given to get'em into the form y=mx+b
3x+2=-16
result > y= -8-3/2x
re-writing it
y=-3/2x-8

i manipulated the other
-2+3y=12
result > y=4+3/2x
re-writing it
y=3/2x+4
Once i have them in this way i compare the slopes (m), if both are equal, they will be parallel and if not, i multiply them together and if the result is -1,
then they are not parallel
they are perpendicular and intercepting
now i have understood what you have explained to me
about m1-m2=-1
 
now i fully understand pka's post at #20
and they are intersecting because two non parallel lines on a Euclidean plane must intersect.
quoting pka '
''Because the slopes are negative reciprocals of each other then the lines are perpendicular.
Then of course they must intersect.''
 
i want to graph the two points to see where they intersect onthe cartesian plane. i wanna do that. let me try it. it is interesting.
for this i was told to graph the two y=mx+b type of equations i got. let's see. i'll report back to you
 
pka said:
To lookagain, Look at this link. Concurrency simply implies intersection.
Click to expand...
let me finish graphing the points to see how they intersect and i will look into your link, for now i can tell you that there is no unanimous accord on this, as far as i see on different articles online. but i treasure your opinion!!!
 
lookagain said:
It's "never give in to." Parallel lines (in the plane) are lines that are the same distance apart, and they do not meet. They do not intersect.
Click to expand...
I was always taught that two lines in the plane are parallel if they have the same slope. There are lines in the plane that have the same slope and intersect. They happen to be the same lines.
 
I just looked up the definition of parallel lines and they all give the definition that lookagain gave.
I still have a problem with this, but I must accept it as it is by definition.
 
Jomo said:
I was always taught that two lines in the plane are parallel if they have the same slope. There are lines in the plane that have the same slope and intersect. They happen to be the same lines.
Click to expand...
interesting!.
 
lookagain said:
It's "never give in to." Parallel lines (in the plane) are lines that are the same distance apart, and they do not meet. They do not intersect.
Click to expand...
Two parallel are always in the same plane because two parallel lines determine a plane: pick two points on one line and any point on the other line, any three non-colinear points determine a plane.
 
i have tried to plot the two slopes -3/2 and 2/3 but i am failing at seeing if they intersect prependicularly.
if you can help me, i appreciate it. thanks. i tried desmos and mathway, but i am doing something wrong, i also tried it on paper and to no avail, they don't look like they intersect perpendicularly, can anyone help, pls?
i tried it following a tutorial on how to graph two linear equations of the form y=mx+ b
i graphed the two equations, but they don't intersect perpendicularly
 
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eddy2017 said:
i have tried to plot the two slopes -3/2 and 2/3 but i am failing at seeing if they intersect prependicularly.
if you can help me, i appreciate it. thanks. i tried desmos and mathway, but i am doing something wrong, i also tried it on paper and to no avail, they don't look like they intersect perpendicularly, can anyone help, pls?
Click to expand...
Did try to plot two LINES?

If yes - what were thr equations of those lines?
 
eddy2017 said:
i have tried to plot the two slopes -3/2 and 2/3 but i am failing at seeing if they intersect prependicularly.
if you can help me, i appreciate it. thanks. i tried desmos and mathway, but i am doing something wrong, i also tried it on paper and to no avail, they don't look like they intersect perpendicularly, can anyone help, pls?
i tried it following a tutorial on how to graph two linear equations of the form y=mx+ b
i graphed the two equations, but they don't intersect perpendicularly
Click to expand...
y=-3/2x - 8
y=3/2x+4
 
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