Had to think about this a little, but here’s my answers
Completely different linear function. After few transformations → y = 3x, so this is completely different than y = → 2x ← + 4
6x -3y = 0
-3y = -6x / : (-3)
y = 3x
it’s y = -2x + 4, very similar to base, looks flipped. Crosses it in (0, 4) point
2x + y = 4
y = -2x + 4
same as base function, so it will be on top of it
8x -4y = -16
-4y = -8x - 16 / : (-4)
y = 2x + 4
Hello! My answers and question are as follows:
6x - 3y = 0
6x - 3(2x + 4) = 0
-12 = 0
The result would make this equation a parallel of y = 2x + 4
2x + y = 4
Rearranging this equation, it would leave us with y = -2x + 4
This would mean that the y-intercept = 4, same as y = 2x + 4, but if I substitute with the y value…
2x + (2x + 4) = 4 —> 4x = 0 —> x = 0; so the intercept point would be (0, 4).
8x - 4y = -16
-4y = -8x - 16
4y = 8x + 16
y = 2x + 4
Since it’s the same equation, this would be infinitely parallel
I have a question though, on the second equation. If I understood correctly, the way to find the x-intercept on any equation would be to y = 0 and resolve it. In the case of y = -2x + 4:
0 = -2x + 4
2x = 4
x = 4/2 —> x = 2
Why is it giving me x = 2 when in fact the x-intercept is actually 0? Thanks in advance!
Did you already draw the curve with for example Geogebra? 
From thereon you can see that the intercept is not at x=0. If you want the y-intercept, set x=0, if you want the x-intercept, set y=0.
Did you already draw the curve with for example Geogebra?
From thereon you can see that the intercept is not at x=0. If you want the y-intercept, set x=0, if you want the x-intercept, set y=0.
Ohhh ok, that makes it a lot clearer haha. The (0,4) is referring to the crossing point between both lines, which is different from the intercepts of each line by itself. Thanks a lot!
I generally agree with your solution but I do believe you made a little math mistake in the first solution. I believe “6x - 3 (2x + 4) = 4” would resolve to “6x - 6x - 12 = 4” rather than “6x - 6x + 12 = 4”. It does however indeed means parallel lines.
The relationships to y = 2x + 4 are:
So I’ve been having a think. I’m not getting algebra at all, I’m watching the vids carefully, sometimes twice, rewinding bits and making lots of notes. I get to the end of the video to the challenge and it appears I don’t have a clue. So I had word with myself and gave myself two choices.
or
Obviously I’m going with option 2. I don’t have time to waste so I’m going to use the course to make myself aware of each topic and carefully watch each lesson and absorb what I can, still taking notes and attempting the challenges but like when my teachers said ‘you wont always have a calculator in your pocket’ and I do. The modern teacher might say ‘you wont always have access to AI and a graphic calculators’ but I will.
If we have some kind of even horizon apocalyptic event then I don’t think algebra is going to help me personally much so from now on I plan to humbly hack my way through my way.
Here is the answer to the Parallel Lines Challenge (using Microsoft Graphing Calculator):
Using ChatGPT to solve and explain the Quiz questions to me:
I feel like I maybe skimped a bit on how I went about it. I took each one and changed it to intercept form and looked at the results compared to our patterns:
For this challenge, I found that:
-The first equation is parallel to the first one, as I got -4 = 0;
-The second equation crosses at the coordinate (0,4).
-The third equation is the same, as using substitution the second equation evaluates to -16 = -16.
I really do not get any of this. I try to follow what you teach, I can see that, but when I see an equation other than the ones you show. I have no idea. I feel like giving up. Very frustrated.
The best thing to do here Richard, if not sure, is plot the equation on paper. This will help you understand what they look like and find the answers to this challenge.
That is one of the problems I seem to have a block, that when I do what is being done on screen I can, but then given an equation to do myself. I have no idea what rule to use and when to plot it.
so, take the equations
I’ll work through one here.
6x - 3y = 0
so, we add 3y to both sizes
so we then have 6x = 3y
we can divide both sides by 3
2x=y
and we can swap the sides around
y = 2x
do the same with 2 and 3 and plot them. Plot points at the original equation in the challenge too and at where X = 0, 2, 4, and 6. This should get you the anwers you need.
Thank you that does help. I will look at them tomorrow.
I have tried what you said, but I get below:
I have even now gone into the blurred out versions and I still do not get it.
the last one has an arithmetic error 16/4 is 4, not 8. This one matches.
Also, 2x + y = 4 becomes y=4-2x which is intersecting
@beegeedee, Thank you for the help. I am still not 100%, but I guess my dyslexcia is not helping.
