Question

solve by graphing:
x+y=1
2x+y=0

I know that the answer is (-1,2)and i know how to mark the spot but can you explain how to draw the lines because i cant figure out the directions it goes in.

Answer 1

To graphing a straight line:

1. Draw your axes.

2. Set x=0 in your equation to get the y-intercept:

x + y = 1
0 + y = 1
y = 1

so we have one point: (0,1)

3. Set y=0 in your equation to get the x-intercept:

x + y = 1
x + 0 = 1
x = 1

so we have a second point: (1.0)

4. Mark the two points on your graph, and use a ruler to draw the straight line that goes through them.

I usually go for the x- and y-intercepts as my points, but any two points will do. Sometimes you can't use two intercepts, as in your second equation:

2x + y = 0

2(0) + y = 0

y = 0

So the origin (0.0) is on this line.
The x- and y-intercepts are the same.
We need another point. No problem; just set x = anything else, for example 3:

2x + y = 0

2*3 + y = 0

y = -6

So we can use the point (3, -6) as our second point. Mark it, and get out the ruler again to draw a straight line through (3, -6) and the origin.

The two lines should meet at the point you expect.