what type of lines are these?

eddy2017 said:
… i think i have to find if they have the same slope. i do that by … putting them in slope intercept [form] …right[?] … confirm this please, i'm looking to go at this step by step …
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You don't need our permission to proceed. Whenever you have an idea, GO FOR IT!

That way, you'll be able to show your work (instead of posting your thoughts).

You'll save time; hence, you'll accomplish more.

?
 
Subhotosh Khan said:
m1 = - 3/2

m2 = 3/2

m1 * m2 is NOT equal to -1 .......... → ........... Hence those are NOT perpendicular l
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so, they are not perpendicular,
so the options that fits the question??
here's the thread question. i know you a re working with different posts so i'm pasting it here again
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
so these two lines are not paralell
they do not intersect perpendicularly, so what's the right answer?
concurrent, i suppose, but i read that for lines to be concurrent there has to be at least three.
 
eddy2017 said:
no, i did not [use graph paper]. i used a graph i did with a ruler.
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When we use rise and run to move from one point on a line to another point, we need to count both horizontal and vertical units. That's not easy to do accurately, when we don't have grid marks to look at.

Do you have a printer?

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i do, but it is not working now. i have to fix it.
i know what you have said. i have studied the topic thoroughly believe me. now i know the lines are not perpendicular to each other. i was trying to prove they were. i thought they were!, but they are not. which makes sense now because i was graphing the slopes right but the graphs were not intersecting perpendicularly.
 
but now i know they are not perpendicular so what are they if they are not parallel either???
 
look at post #52 i posted them right there
this has been frustrating!
 
eddy2017 said:
… if you are going to help get serious about it
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We pointed out your mistake (writing 3/2 instead of 2/3). What additional help do you need, in order to correct that mistake?

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Otis said:
We pointed out your mistake (writing 3/2 instead of 2/3). What additional help do you need, in order to correct that mistake?

\(\;\)
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the question has not been answered!!!!
what is the option that fits and why
 
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?
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If 2 parallel lines have an intersection, then they are the same line. A line can be written with infinite values of A, B, and C. For example:

2x + 3y = 5 and 4x + 6y = 10 and -6x - 9y = -15

are the same line. If you multiply every term of the equation by the same factor different from zero, you will get the same line.

You don´t need to work with the slope if you want to determine if 2 lines are parallel or perpendicular. If you have

[MATH]A_1x+B_1y=C_1[/MATH]
and

[MATH]A_2x+B_2y=C_2[/MATH]
Then, if [MATH]A_1*B_2=A_2*B_1[/MATH] they are parallel. If [MATH]A_1*A_2+B_1*B_2=0[/MATH] they are perpendicular. If they are parallel, and they share one point, they are the same line.
 
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