Question
Graph by plotting points.
y = −2x+3
y = −2x+3
Answers
GPT-4o mini
To graph the equation \( y = -2x + 3 \), we can follow these steps:
1. **Identify Two Points**: We can find points by choosing different values for \( x \) and calculating the corresponding \( y \) values.
- **Point 1**: Let \( x = 0 \):
\[
y = -2(0) + 3 = 3
\]
So, the first point is \( (0, 3) \).
- **Point 2**: Let \( x = 1 \):
\[
y = -2(1) + 3 = -2 + 3 = 1
\]
So, the second point is \( (1, 1) \).
- **Point 3**: Let \( x = 2 \):
\[
y = -2(2) + 3 = -4 + 3 = -1
\]
So, the third point is \( (2, -1) \).
2. **Plot the Points**: On a Cartesian coordinate system:
- Plot \( (0, 3) \)
- Plot \( (1, 1) \)
- Plot \( (2, -1) \)
3. **Draw the Line**: Connect the points with a straight line. Since this is a linear equation, the points will form a straight line.
### Summary of Points:
- \( (0, 3) \)
- \( (1, 1) \)
- \( (2, -1) \)
### Graphical Representation:
If you were to visualize it, you should see a line that slopes downward from left to right, starting at \( (0, 3) \) and descending as \( x \) increases.
1. **Identify Two Points**: We can find points by choosing different values for \( x \) and calculating the corresponding \( y \) values.
- **Point 1**: Let \( x = 0 \):
\[
y = -2(0) + 3 = 3
\]
So, the first point is \( (0, 3) \).
- **Point 2**: Let \( x = 1 \):
\[
y = -2(1) + 3 = -2 + 3 = 1
\]
So, the second point is \( (1, 1) \).
- **Point 3**: Let \( x = 2 \):
\[
y = -2(2) + 3 = -4 + 3 = -1
\]
So, the third point is \( (2, -1) \).
2. **Plot the Points**: On a Cartesian coordinate system:
- Plot \( (0, 3) \)
- Plot \( (1, 1) \)
- Plot \( (2, -1) \)
3. **Draw the Line**: Connect the points with a straight line. Since this is a linear equation, the points will form a straight line.
### Summary of Points:
- \( (0, 3) \)
- \( (1, 1) \)
- \( (2, -1) \)
### Graphical Representation:
If you were to visualize it, you should see a line that slopes downward from left to right, starting at \( (0, 3) \) and descending as \( x \) increases.