Graph a proportional relationship y=2x by plotting points

Answer 1

Sure, I'd be happy to help you graph the proportional relationship \( y = 2x \) by plotting points.

First, let's plot some points. We'll choose several values for \( x \) and calculate the corresponding \( y \)-values using the equation \( y = 2x \).

1. Let \( x = -2 \):
\[
y = 2(-2) = -4
\]
Point: \((-2, -4)\)

2. Let \( x = -1 \):
\[
y = 2(-1) = -2
\]
Point: \((-1, -2)\)

3. Let \( x = 0 \):
\[
y = 2(0) = 0
\]
Point: \((0, 0)\)

4. Let \( x = 1 \):
\[
y = 2(1) = 2
\]
Point: \((1, 2)\)

5. Let \( x = 2 \):
\[
y = 2(2) = 4
\]
Point: \((2, 4)\)

Now that we have several points, we can plot them on a graph:

1. \((-2, -4)\)
2. \((-1, -2)\)
3. \((0, 0)\)
4. \((1, 2)\)
5. \((2, 4)\)

When you plot these points on a coordinate plane, you should see that they form a straight line. Since this is a proportional relationship, the line should pass through the origin \((0,0)\) and have a constant rate of change (slope). In this case, the slope \( m = 2 \) means for every unit increase in \( x \), \( y \) increases by 2 units.

Here's a basic visual representation (without an actual graph):

```
y
| *
| *
| *
| *
| *
|
|------------------x
```

In your graphing paper or digital graphing tool, draw the x-axis and y-axis, mark the points as listed, and draw a straight line through them. The line you draw will represent the equation \( y = 2x \).