how to draw a graph of line 2x-y=3
Answers
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!