Can someone please explain how to solve this problem? I don't remember planes...

In the xy-plane, what is the slope of the line whose equation is 3x-2y=8?

Question

Can someone please explain how to solve this problem? I don't remember planes...

In the xy-plane, what is the slope of the line whose equation is 3x-2y=8?

jim_thompson5910 · Answer

First solve for y. Do you know how to do this?

anonymous · Answer

I think so, like this?:
subtract 3x from each side:
-2y=8-3x  divide each side by -2
y=8-3x
    |dw:1345662293560:dw|
      -2

anonymous · Answer

um, that didn't come out right. I was trying to show that 8-3x is over -2

jim_thompson5910 · Answer

like this 

$$\Large 3x-2y=8$$


$$\Large -2y=8-3x$$


$$\Large y=\frac{8-3x}{-2}$$

??

anonymous · Answer

precisely

jim_thompson5910 · Answer

Keep going and simplify it into y = mx+b form

anonymous · Answer

THAT I don't know

jim_thompson5910 · Answer

$$\Large 3x-2y=8$$ 


$$\Large -2y=8-3x$$ 


$$\Large y=\frac{8-3x}{-2}$$


$$\Large y=\frac{-3x+8}{-2}$$


$$\Large y=\frac{-3x}{-2}+\frac{8}{-2}$$


$$\Large y=\frac{3}{2}x-4$$


Notice how the last equation is in y = mx+b form where m = 3/2 and b = -4

anonymous · Answer

Ok, I guess that could make sense. But then what does that mean? I still don't understand where y is if I were to chart it on the graph

anonymous · Answer

and what does "slope of the line" mean?

jim_thompson5910 · Answer

y = mx+b is the general equation of any line

jim_thompson5910 · Answer

The value of m is the slope

jim_thompson5910 · Answer

The point (0,b) is the y-intercept

anonymous · Answer

Ok, so 3/2 is the slope then?

jim_thompson5910 · Answer

yes, this represents how "steep" or "shallow" the line is

jim_thompson5910 · Answer

it also represents if the line goes up or down (as you read it from left to right)

anonymous · Answer

ok, so if I were to graph this, what would it look like?

jim_thompson5910 · Answer

You would plot a point at (0,-4), which is the y-intercept

phi · Answer

Here is a video, on graphing http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/v/graphs-using-slope-intercept-form he also has other videos about lines that might be helpful

jim_thompson5910 · Answer

Then you would go up 3 units, then to the right 2 units to get to the next point (2, -1)

jim_thompson5910 · Answer

You now have two points. Draw a straight line through them to graph the line.

anonymous · Answer

Cool, thank you for all your help, jim! 
Also, thank you, phi for the vid link, I'll check it out :)

jim_thompson5910 · Answer

you're welcome

phi · Answer

This one looks more appropriate for how to graph the line http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/v/algebra--graphing-lines-1