Question

Graph the proportional relationship y = — 2x by plotting points.
A. Graph points: (0, 0) (1, 5) (2, 10)
B. Graph

Answer 1

To graph the proportional relationship described by the equation \( y = -2x \), you should plot various points that satisfy this equation.

### Step 1: Identify Points
Let’s calculate some points by substituting different values of \( x \):

1. **For \( x = 0 \):**
\[
y = -2(0) = 0 \quad \Rightarrow \quad (0, 0)
\]

2. **For \( x = 1 \):**
\[
y = -2(1) = -2 \quad \Rightarrow \quad (1, -2)
\]

3. **For \( x = 2 \):**
\[
y = -2(2) = -4 \quad \Rightarrow \quad (2, -4)
\]

4. **For \( x = -1 \):**
\[
y = -2(-1) = 2 \quad \Rightarrow \quad (-1, 2)
\]

5. **For \( x = -2 \):**
\[
y = -2(-2) = 4 \quad \Rightarrow \quad (-2, 4)
\]

### Step 2: Plotting the Points
You should plot the points on a Cartesian coordinate plane. The relevant points based on our calculations would be:
- (0, 0)
- (1, -2)
- (2, -4)
- (-1, 2)
- (-2, 4)

### Step 3: Draw the Line
Once you've plotted all the points, draw a straight line through all of them. The line will extend infinitely in both directions. The line will be descending because as \( x \) increases, \( y \) decreases due to the negative slope.

### Visual Representation
Here's a simple representation (text-based) of what the graph might look like:

```
y
|
4 - * (-2, 4)
3 -
2 - * (-1, 2)
1 -
0 - * (0, 0)
-1 -
-2 - * (1, -2)
-3 -
-4 - * (2, -4)
-------------
-2 -1 0 1 2 x
```

### Note
You mentioned graphing points (0, 0), (1, 5), (2, 10), which do not correspond to the equation \(y = -2x\). Please ensure you're using points that satisfy the equation \(y = -2x\) for correct plotting.