I would like to point out that $y=\frac{1}{3x}-6$y=13x−6, does NOT produce a straight line. The graph below shows what it looks like (the red curve)
How do you get this? You can start with $y=\frac{1}{x}$y=1x , it should be a curve which approaches y=0 as x goes to infinity, and y goes to infinity as x approaches 0. To draw it, you can take sample points like x= 1, y=1, and x = 2, y = 1/2, and x = 0.5, y =2, and so on. Plotting it gives the green curve below.
Then divide by 3 to get $y=\frac{1}{3x}$y=13x , which is simply the same curve as 1/x, but vertically squished by a factor of 3. That gives you the blue/purple curve (I'm bad with colors, sorry). Notice that y= 1/3 when x=1, in this new curve.
As a final step, subtract 6 - all this does is vertically shifts the entire curve 6 units down on the y-axis, giving the red curve.
6 years ago
Answered By Xuezhong J
y=1/3x-6 is a straight line, only need 2 points to determine this line. x=0, y=-6; x=18, y=0.
Attached Whiteboard:
Play Drawing6 years ago
Answered By Kazi A
I would like to point out that $y=\frac{1}{3x}-6$y=13x −6, does NOT produce a straight line. The graph below shows what it looks like (the red curve)
How do you get this? You can start with $y=\frac{1}{x}$y=1x , it should be a curve which approaches y=0 as x goes to infinity, and y goes to infinity as x approaches 0. To draw it, you can take sample points like x= 1, y=1, and x = 2, y = 1/2, and x = 0.5, y =2, and so on. Plotting it gives the green curve below.
Then divide by 3 to get $y=\frac{1}{3x}$y=13x , which is simply the same curve as 1/x, but vertically squished by a factor of 3. That gives you the blue/purple curve (I'm bad with colors, sorry). Notice that y= 1/3 when x=1, in this new curve.
As a final step, subtract 6 - all this does is vertically shifts the entire curve 6 units down on the y-axis, giving the red curve.
Attached Graph: