Y=x+2 on a graph

Answer 1

Certainly! The equation \( Y = x + 2 \) is a linear equation, which means its graph will be a straight line. Here’s how to graph it:

### Step-by-Step Graphing

1. **Identify the slope and y-intercept:**
- The equation is in the slope-intercept form \( Y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
- Here, \( m = 1 \) (slope) and \( b = 2 \) (y-intercept).

2. **Plot the y-intercept:**
- The y-intercept (\( b \)) is the point where the line crosses the y-axis.
- For \( b = 2 \), plot the point (0, 2).

3. **Use the slope to find another point:**
- The slope \( m = 1 \) indicates a rise/run of 1/1. This means for every 1 unit increase in \( x \), \( Y \) increases by 1 unit.
- Starting from (0, 2), if you move 1 unit to the right (x = 1), then move 1 unit up (Y = 3). Plot this point (1, 3).

4. **Draw the line:**
- Connect the two points (0, 2) and (1, 3) with a straight line.
- Extend the line in both directions.

### Points on the Line

Here are a few points that lie on the line \( Y = x + 2 \):
- When \( x = -2 \), \( Y = -2 + 2 = 0 \). Point: (-2, 0)
- When \( x = 0 \), \( Y = 2 \). Point: (0, 2)
- When \( x = 2 \), \( Y = 2 + 2 = 4 \). Point: (2, 4)

### Graph Representation

You can sketch or plot these points on a coordinate plane:

Y
^
|
6-|
5-|
4-| * (2, 4)
3-| * (1, 3)
2-| * (0, 2)
1-|
|_________________> X
-2 -1 0 1 2 3 4

By connecting the points you’ve plotted, you'll see that they form a straight line. This line is the graph of the equation \( Y = x + 2 \).