what is the graph of the direct variation equation y=5/2x
The graph of the direct variation equation y = (5/2)x is a line that passes through the origin (0,0) and has a slope of 5/2. It is a straight line that increases as x increases and decreases as x decreases.
To graph the equation y = (5/2)x, we can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope is (5/2), which means that for every unit increase in x, the corresponding y-value increases by (5/2) units.
To plot the graph, we can start by finding a few points. Let's choose x = 0, 1, 2, -1, and -2:
For x = 0:
y = (5/2)(0) = 0
So the point (0, 0) is on the graph.
For x = 1:
y = (5/2)(1) = 5/2
So the point (1, 5/2) is on the graph.
For x = 2:
y = (5/2)(2) = 5
So the point (2, 5) is on the graph.
For x = -1:
y = (5/2)(-1) = -5/2
So the point (-1, -5/2) is on the graph.
For x = -2:
y = (5/2)(-2) = -5
So the point (-2, -5) is on the graph.
Now, we can plot these points on a coordinate system and draw a line passing through them. The graph will be a straight line because this equation represents a direct variation.
Here is the graph of y = (5/2)x:
```
|
5 | .
|
4 |
|
3 |
|
2 |
| .
1 |
|
0 | .
-2 -1 0 1 2 ...
```
Note that this line passes through the origin (0, 0), which is common for direct variation equations.