To graph the equation x + 2y - 1 = 9, we can first rearrange it to solve for y:
x + 2y - 1 = 9
2y = 10 - x
y = (10 - x) / 2
Now we can pick three different values of x and find the corresponding values of y using this equation. Let's choose x = 0, x = 2, and x = 4:
When x = 0:
y = (10 - 0) / 2 = 5
So one point on the graph is (0, 5).
When x = 2:
y = (10 - 2) / 2 = 4
So another point on the graph is (2, 4).
When x = 4:
y = (10 - 4) / 2 = 3
So the third point on the graph is (4, 3).
To check if this equation is linear or nonlinear, we can see if it satisfies the property of linearity, which is that if we draw a line between any two points on the graph, all other points on the graph should lie on that same line.
Let's check if this holds true for the three points we've chosen:
If we plot these three points, we get:
|
6 |
| * (4, 3)
5 |
| * (2, 4)
4 |
| * (0, 5)
3 +------------------
0 2 4 6 8 10
Visually inspecting the plot, it looks like all three points do indeed lie on a straight line. Therefore, we can conclude that this equation is linear.