SOLUTION: How do I graph the linear equation 3x + 2y = 6 by plotting 5 points. You must choose at least one negative x value. Show the points as ordered pairs. Thanks for your help

Algebra ->  Coordinate-system -> SOLUTION: How do I graph the linear equation 3x + 2y = 6 by plotting 5 points. You must choose at least one negative x value. Show the points as ordered pairs. Thanks for your help      Log On


   

Question 84439: How do I graph the linear equation 3x + 2y = 6 by plotting 5 points. You must choose at least one negative x value. Show the points as ordered pairs. Thanks for your help
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, convert the the equation to slope-intercept form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)


3x%2B2y=6 Start with the given equation


3x%2B2y-3x=6-3x Subtract 3x from both sides


2y=-3x%2B6 Simplify


%282y%29%2F%282%29=%28-3x%2B6%29%2F%282%29 Divide both sides by 2 to isolate y


y+=+%28-3x%29%2F%282%29%2B%286%29%2F%282%29 Break up the fraction on the right hand side


y+=+%28-3%2F2%29x%2B3 Reduce and simplify


The original equation 3x%2B2y=6 (standard form) is equivalent to y+=+%28-3%2F2%29x%2B3 (slope-intercept form)


The equation y+=+%28-3%2F2%29x%2B3 is in the form y=mx%2Bb where m=-3%2F2 is the slope and b=3 is the y intercept.





Now in order to graph y=%28-3%2F2%29x%2B3, we need to plot some points.

So we can start at any x value. So lets start at x=-4

y=%28-3%2F2%29x%2B3 Start with the given equation

y=%28-3%2F2%29%28-4%29%2B3 Plug in x=-4

%28-3%2F2%29%28-4%29%2B3=9 Calculate the y value
So when x=-4 y=9
So our 1st point is (-4,9)




y=%28-3%2F2%29x%2B3 Start with the given equation

y=%28-3%2F2%29%28-2%29%2B3 Plug in x=-2

%28-3%2F2%29%28-2%29%2B3=6 Calculate the y value
So when x=-2 y=6
So our 2nd point is (-2,6)




y=%28-3%2F2%29x%2B3 Start with the given equation

y=%28-3%2F2%29%280%29%2B3 Plug in x=0

%28-3%2F2%29%280%29%2B3=3 Calculate the y value
So when x=0 y=3
So our 3rd point is (0,3)




y=%28-3%2F2%29x%2B3 Start with the given equation

y=%28-3%2F2%29%282%29%2B3 Plug in x=2

%28-3%2F2%29%282%29%2B3=0 Calculate the y value
So when x=2 y=0
So our 4th point is (2,0)




y=%28-3%2F2%29x%2B3 Start with the given equation

y=%28-3%2F2%29%284%29%2B3 Plug in x=4

%28-3%2F2%29%284%29%2B3=-3 Calculate the y value
So when x=4 y=-3
So our 5th point is (4,-3)




y=%28-3%2F2%29x%2B3 Start with the given equation

y=%28-3%2F2%29%286%29%2B3 Plug in x=6

%28-3%2F2%29%286%29%2B3=-6 Calculate the y value
So when x=6 y=-6
So our 6th point is (6,-6)






Now lets make a table of the values we have calculated 



 xy



 -49
 

 -26
 

 03
 

 20
 

 4-3
 

 6-6
Now plot the points

Now connect the points, this is the graph of %28-3%2F2%29x%2B3