How do you graph 2x + y = 3 by plotting points?

1 Answer
Mar 25, 2017

Find a few (x,y) pairs that satisfy the equation; plot these points; connect them.

Explanation:

Pick some values for x, and use the equation to find what y must be for each of those x's.

For example, if x is 0, then we have:

"         "2x+y=3
=>2(0)+y=3
=>"     "0+y=3
=>"            "y=3

So when x=0, we have y=3. Meaning the point (x,y)=(0,3) is a solution to 2x+y=3, and so our graph of the equation will pass through (0,3).

We can get a few more points:

If x=1, then

"         "2x+y=3
=>2(1)+y=3
=>"     "2+y=3
=>"            "y=1

So (x,y)=(1,1) is also on our graph.

Similarly, if x=2, then we get y="–"1, giving us the point (x,y)=(2,"–"1).

We then take the points we've computed, (0,3), (1,1), (2,"–"1), and plot them on a graph:

graph{((x)^2+(y-3)^2-.02)((x-1)^2+(y-1)^2-.02)((x-2)^2+(y+1)^2-.02)=0 [-10, 10, -5, 5]}

Last, since we know this equation is linear, we just need to connect the dots with a line:

graph{((x)^2+(y-3)^2-.02)((x-1)^2+(y-1)^2-.02)((x-2)^2+(y+1)^2-.02)(2x+y-3)=0 [-10, 10, -5, 5]}

And we're done!