Question
Graph the proportional relationship y=−2x by plotting points. show on a graph
Answers
GPT-4o mini
To graph the proportional relationship given by the equation \( y = -2x \), we can start by plotting a few points that satisfy this equation.
### Step 1: Choose values for \( x \).
We'll choose a range of \( x \) values, including both positive and negative values, as well as zero:
- Let \( x = -2 \):
\[
y = -2(-2) = 4 \quad \Rightarrow \quad (-2, 4)
\]
- Let \( x = -1 \):
\[
y = -2(-1) = 2 \quad \Rightarrow \quad (-1, 2)
\]
- Let \( x = 0 \):
\[
y = -2(0) = 0 \quad \Rightarrow \quad (0, 0)
\]
- Let \( x = 1 \):
\[
y = -2(1) = -2 \quad \Rightarrow \quad (1, -2)
\]
- Let \( x = 2 \):
\[
y = -2(2) = -4 \quad \Rightarrow \quad (2, -4)
\]
### Step 2: Plot these points.
Now, we can plot the points \((-2, 4)\), \((-1, 2)\), \((0, 0)\), \((1, -2)\), and \((2, -4)\) on a graph.
### Step 3: Draw the line.
Once the points are plotted, we can draw a straight line through them.
### Visualization of the Graph
You can create the graph using graphing tools, plotting software, or manually on graph paper. Here’s how the graph would look like:
1. The y-axis (vertical) and x-axis (horizontal) should be clearly marked.
2. Each point should be plotted accurately according to the coordinates.
3. Since it's a linear equation, the points will form a straight line which should extend in both directions (indicated with arrows at both ends).
**Note**: Unfortunately, I don't have the capability to create visual images or graphs directly. You can use graphing software or plot it by hand based on the instructions above. The line will slope downwards due to the negative coefficient of \( x \), demonstrating the inverse proportional relationship where \( y \) decreases as \( x \) increases.
### Step 1: Choose values for \( x \).
We'll choose a range of \( x \) values, including both positive and negative values, as well as zero:
- Let \( x = -2 \):
\[
y = -2(-2) = 4 \quad \Rightarrow \quad (-2, 4)
\]
- Let \( x = -1 \):
\[
y = -2(-1) = 2 \quad \Rightarrow \quad (-1, 2)
\]
- Let \( x = 0 \):
\[
y = -2(0) = 0 \quad \Rightarrow \quad (0, 0)
\]
- Let \( x = 1 \):
\[
y = -2(1) = -2 \quad \Rightarrow \quad (1, -2)
\]
- Let \( x = 2 \):
\[
y = -2(2) = -4 \quad \Rightarrow \quad (2, -4)
\]
### Step 2: Plot these points.
Now, we can plot the points \((-2, 4)\), \((-1, 2)\), \((0, 0)\), \((1, -2)\), and \((2, -4)\) on a graph.
### Step 3: Draw the line.
Once the points are plotted, we can draw a straight line through them.
### Visualization of the Graph
You can create the graph using graphing tools, plotting software, or manually on graph paper. Here’s how the graph would look like:
1. The y-axis (vertical) and x-axis (horizontal) should be clearly marked.
2. Each point should be plotted accurately according to the coordinates.
3. Since it's a linear equation, the points will form a straight line which should extend in both directions (indicated with arrows at both ends).
**Note**: Unfortunately, I don't have the capability to create visual images or graphs directly. You can use graphing software or plot it by hand based on the instructions above. The line will slope downwards due to the negative coefficient of \( x \), demonstrating the inverse proportional relationship where \( y \) decreases as \( x \) increases.