what type of lines are these?

eddy2017

eddy2017

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Hi, I'm doing this exercise.
equation A : 3x+2y=-16
equation B: -2x+3y=12
what type of lines are these equations
options
a) parallel
b) concurrent
c) parallel and intercepting
d)perpendicular and intercepting
okay i am reading a little bit about these type of lines to be able to do answer.
i need your direction though.
to know if they are parallel lines i think i have to find if they have the same slope. i do that by manipulating the two equations given and putting them in slope intercept to compare both slopes, right,
confirm this please,.
i'm looking to go at this step by step.
thanks for any hint
 
i think they are not parallel because they do not have the same slope
3x + 2= -16 this one is already in slope intercept form, where m=3
the other
-2x + 3y=12
this one i have to manipulate into slope intercept form,
-2x + 3y=12
+2x +2x
3y=12 +2x
i'll rewrite this
3y=2x+12
isolating y
1/3(3y)= 1/3(2x+12)
y= 2/3x + 4
now this one is in y=mx+b form and i see that m=2/3
so these slopes are different so they are not parallel.

now, how do i go about finding if they are concurrent,
well, i have read this:
'A set of lines or curves are said to be concurrent if they all intersect at the same point. In the figure below, the three lines are concurrent because they all intersect at a single point P. The point P is called the "point of concurrency'
but these lines are parallel so they never intersect, right, so this option off the table. (no)

parallel and intercepting is out the window too cos
'In the Euclidean plane, parallel lines don't intersect. Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction. If they intersect, then you don't call them parallel.

so they must be perpendicular and intercepting
but how can i go about mathematically proving that it is a fact?
 
Last edited:
eddy2017 said:
Hi, I'm doing this exercise.
equation A : 3x+2y=-16
equation B: -2x+3y=12
Click to expand...
If [MATH]Ax+By+C=0[/MATH] is a line then if [MATH]A\cdot B\ne 0[/MATH] then the slope of that line is [MATH]m=\dfrac{-A}{B}[/MATH].
You need to try again.
 
eddy2017 said:
i think they are not parallel because they do not have the same slope
3x + 2= -16 this one is already in slope intercept form, where m=3
the other
-2x + 3y=12
this one i have to manipulate into slope intercept form,
-2x + 3y=12
+2x +2x
3y=12 +2x
i'll rewrite this
3y=2x+12
isolating y
1/3(3y)= 1/3(2x+12)
y= 2/3x + 4
now this one is in y=mx+b form and i see that m=2/3
so these slopes are different so they are not parallel.

now, how do i go about finding if they are concurrent,
well, i have read this:
'A set of lines or curves are said to be concurrent if they all intersect at the same point. In the figure below, the three lines are concurrent because they all intersect at a single point P. The point P is called the "point of concurrency'
but these lines are parallel so they never intersect, right, so this option off the table. (no)

parallel and intercepting is out the window too cos
'In the Euclidean plane, parallel lines don't intersect. Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction. If they intersect, then you don't call them parallel.

so they must be perpendicular and intercepting
but how can i go about mathematically proving that it is a fact?
Click to expand...
You have calculated incorrectly. ........................... edited

The slope of line (1) is m1 = -(3/2) .....&....... the slope of line (2) is m2 = (2/3) ... → ... m1 * m2 = -1 ... This is the sufficient condition for two planer lines to be perpendicular to each other.
 
Last edited by a moderator:
This is the sufficient condition for two planer lines to be perpendicular to each other.

But why?. I need to understand the reason why they are!. [perpendicular to each
other and and intercepting]
Drop me a hint at least.

And pka is not agreeing with the way I performed it
 
Subhotosh Khan said:
You have calculated correctly.

The slope of line (1) is m1 = -(3/2) .....&....... the slope of line (2) is m2 = (2/3) ... → ... m1 * m2 = -1 ... This is the sufficient condition for two planer lines to be perpendicular to each other.
Click to expand...
eddy said that the slope of line 1 was 3, not -3/2
 
i assumed this equation to be in slope intercept form, which gives m as 3.
3x + 2= -16
and i thought the other given had to be put in slope int form
2x + 3y=12
that is why i tried and manipulate it to get into slope int form
the m rersulted to be 2/3 so i concluded that the two slopes being different the lines could not be parallel.

is this right or wrong?

let's take it step by step, please, follow my questions so i be able to understand.
then i gave some reasoning for them not to be concurrrent and and not to be, of course, parallel and intercepting
tell me if my work is not true, and where i failed so i can fix it.
 
@ pka post#3
but you did not tell me what was wrong. you wrote the equation for standard form but you did not tell me where i went wrong and why my analysis failed..
 
i know choice d is the right answer but i am trying to get help to demonstrate it,that is, if my analysis in working was the slopes was correct.
i know t his :
Yes, for two lines to be perpendicular to each other, they must always intersect each other at 90 degrees.
 
You say that the slope of 3x + 2= -16 is 3.
If I multiply both sides by 5 the equation becomes 15x + 10 = -80. So now the slope is 15?
What if I multiplied by 0.5. The equation becomes 1.5x+ 1 = -8. Now the slope is 1.5?
If I multiple both sides by 7 the eq becomes 21x+14 = -112. Now the slope is 21?
How can this line have so many slopes?
 
3x-2y=-16
this is the right equation. i'm rectifiying
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
the slope is -3/2

and the other was 2/3
so the lines are not parallel cos the slope is not the same
-3/2 is not equal to 2/3
so i know they are NOT parallel. ..................................................edited
i want to prove now that they are not concurrent.
if this is okay,
then drop me a hint to prove they are or not concurrent, if you will.
 
Last edited by a moderator:
i can only think of this, analysing something i read:
'It is commonly known that two non-parallel intersect at one point. If a third line is formed passing through one common point or intersecting each other at one common point, then these straight lines are termed as concurrent lines.'

so, there is no third line mentioned here, so these lines are not concurrent.
 
eddy2017 said:
i can only think of this, analysing something i read:
'It is commonly known that two non-parallel intersect at one point. If a third line is formed passing through one common point or intersecting each other at one common point, then these straight lines are termed as concurrent lines.'

so, there is no third line mentioned here, so these lines are not concurrent.
Click to expand...
Two intersecting lines are concurrent lines.
 
how can i prove they intersect?
if this is true, and it is, how can i demonstrate it?
''lines that pass through a single point, on a cartesian plane, are called concurrent lines. The point through which the concurrent lines pass is called the point of concurrency.All the intersecting lines or non-parallel lines are concurrent. ''
i want to prove to myself they intersect. how can i do it?
 
is this a good start?
How Do I Find the Point of Intersection of Two Lines?
  1. Get the two equations for the lines into slope-intercept form. ...
  2. Set the two equations for y equal to each other.
  3. Solve for x. ...
  4. Use this x-coordinate and substitute it into either of the original equations for the lines and solve for y.
okay, i'll try to do it. if i get stuck i'll let you know. thanks a lot, Dr Khan
 
eddy2017 said:
Hi, I'm doing this exercise.
equation A : 3x+2y=-16
equation B: -2x+3y=12
what type of lines are these equations
options
a) parallel
b) concurrent
c) parallel and intercepting
d)perpendicular and intercepting
okay i am reading a little bit about these type of lines to be able to do answer.
i need your direction though.
to know if they are parallel lines i think i have to find if they have the same slope. i do that by manipulating the two equations given and putting them in slope intercept to compare both slopes, right,
confirm this please,.
i'm looking to go at this step by step.
thanks for any hint
Click to expand...
Choice 'c' cannot happen - from the definition of parallel line in a plane.
 
eddy2017 said:
@ pka post#3
but you did not tell me what was wrong. you wrote the equation for standard form but you did not tell me where i went wrong and why my analysis failed..
equation A : 3x+2y=-16
equation B: -2x+3y=12
Click to expand...
the slope of equation A is [MATH]m_A=\dfrac{-3}{2}[/MATH]the slope of equation B is [MATH]m_B=\dfrac{2}{3}[/MATH]Because the slopes are negative reciprocals of each other then the lines are perpendicular.
Then of course they must intersect.
 
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