y = 3x + 1 and 3y - 9x = 7, are the lines parallel?

[@tomtke7351]

classic: y = mx + b where m is slope delta-y/delta-x and y intercept (when x = 0) is b given, here, are two equations y = 3x + 1 eq.1 3y - 9x = 7 eq.2 rearrange eq.2 3y = 9x + 7 y = 3x + (7/3) eq.2 both equations have same slope (m = 3) So YES! Lines are parallel eq.1 y-intercept = 1 eq.2 y-intercept = 7/3

[@sergiodario58able]

Yes they are. Just divide the second equation by 3 to isolate the Y variable, and you get the same slope of 3. Just with different Y intercept.

[@lauriejerome9179]

Great explanation! Thank you.

[@gregorytrane7828]

Excellent!

[@kennethwright870]

Yes, they have the same slope, 3, and cross the y-axis at different points.

[@susanm1109]

They are parallel because they have the same slope (3/1). The first has y-intercept of 1 and the second has y-intercept 7/3.

[@piezoification]

Was it wrong to divide out by 3?

[@NC4U2b]

And the circled “therefore” looks something like a bowling ball (if the fingers going into the not-the-thumb holes are oddly somewhat far apart!)! 😂

[@NC4U2b]

🎳 (maybe you could PIN this reply! (See 11:37 in the video.)

[@ChavoMysterio]

y=3x+1 3y-9x=7 3(3x+1)-9x=7 9x+3-9x=7 3=7 false statement Yes, the lines are parallel.

[@tonitalas1757]

Yes slope of 3

[@Kedatgahbelu12]

They should be parallel. As long as the slopes of these two functions have the same ratio of positive 3/1.

[@piezoification]

Why not define a "linear equation"

[@BrickEngines]

These are parallel because they have the same ratio, let me explain: the first one has a ratio of 3/1 and it’s +1 in the y plane, the second one if you simplify you can notice it has the same ratio (y=3/1x + 7/3) and this one is + 7/3 in the y plane. So in conclusion the two lines are parallel because they have the same ratio.

[@BrickEngines]

I don’t know the technical word for what I mean ratio but you probably get it.

[@BrickEngines]

Second equations calculation: 3y-9x=7 3y=7+9x y= (7+9x)/3 y= 7/3 + 3x

[@shariecebrewster5962]

O am there's

[@porusrabadi7024]

Obviously parallel. The slope is the same. Video too long for such a simple rider.

[@DavidLee-qe3rd]

This would have been much more useful without the 12 minutes of pointless waffle!