Can someone answer this including explaining steps

Question

Find three points on the line 2x+3y=1

Answer 1

Simply assign arbitrary numbers to x( whatever you like) and solve for y.

If plugging x, you find y, point (x,y) is located on the line.

Ok, lets try out some numbers:

x=2 --> 2(2)+3y=1  --> 3y=-3 --> y=-1 ===> (2,-1) is on the line

x=-1  --> 2(-1)+3y=1   --> 3y=3 --> y=1  ===> (-1,1) is on the line

x=0 --> 2(0)+3y=1  -->  3y=1 --> y=1/3 ===> (0,1/3) is on the line

Answer 2

Lines go on indefinitely in either direction.  Basically, you can pick ANY value for x that you choose...and you can calculate the corresponding y value.  Since you are only asked for three, I would keep the math simple, and choose x=0,1, and 2.

 

• For x=0, just plug it in.  
• 2(0)+3y=1
• 0+3y=1
• 3y=1
• y=1/3
• Our first point is (0,1/3)

 

• x=1
• 2(1)+3y=1
• 2+3y=1
• 3y=-1
• y=-1/3
• Second point (1,-1/3)

 

• x=2
• 2(2)+3y=1
• 4+3y=1
• 3y=-3
• y=-1
• Third point (2,-1)

 

Again, it's very important to understand that I could choose ANY x value.  Here's another totally random point that would also be correct.

 

• x=50.5
• 2(50.5)+3y=1
• 101+3y=1
• 3y=-100
• y=-100/3, or =-33 1/3
• (50.5, -100/3) also on this line