Algebra 1 Practice - Graph a Linear Function by Making a Table (Example 1)

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To graph a linear function by making a table, follow these detailed steps:

### **1. Write Down the Linear Function**

Start with the linear function in the form \( y = mx + b \), where:
- \( m \) is the slope of the line.
- \( b \) is the y-intercept.

### **2. Create a Table of Values**

1. **Choose x-values**: Select a set of x-values. Typically, you choose at least three x-values to ensure accuracy. It's helpful to include negative, zero, and positive values.

2. **Calculate Corresponding y-values**:
- Substitute each chosen x-value into the linear function to find the corresponding y-value.
- For each x-value, compute \( y \) using the formula \( y = mx + b \).

3. **Fill in the Table**:
- List each x-value and its corresponding y-value in a table format.

**Example**:
For the function \( y = 2x + 1 \):

| x | y |
|----|-----|
| -1 | -1 |
| 0 | 1 |
| 1 | 3 |

- For \( x = -1 \): \( y = 2(-1) + 1 = -2 + 1 = -1 \)
- For \( x = 0 \): \( y = 2(0) + 1 = 0 + 1 = 1 \)
- For \( x = 1 \): \( y = 2(1) + 1 = 2 + 1 = 3 \)

### **3. Plot the Points**

1. **Draw the Coordinate Plane**: Draw a horizontal axis (x-axis) and a vertical axis (y-axis) on graph paper or a digital graphing tool.

2. **Plot Each Ordered Pair**:
- Locate each point from the table on the coordinate plane.
- Mark each point with a dot and label it if necessary.

### **4. Draw the Line**

1. **Connect the Points**: Use a ruler to draw a straight line through the plotted points. Since it's a linear function, the points should lie on a straight line.

2. **Extend the Line**: Extend the line beyond the points in both directions, and add arrowheads at the ends to indicate that the line continues indefinitely.

### **5. Label the Graph**

1. **Add Labels**: Label the x-axis and y-axis, and write the equation of the line on the graph.

2. **Check Accuracy**: Verify that the points on the line match the table values and that the line is straight.

### **Summary**:

To graph a linear function:
- Create a table with chosen x-values and calculate their corresponding y-values.
- Plot these (x, y) points on a coordinate plane.
- Draw a straight line through the points and extend it.

This method ensures an accurate and clear representation of the linear function.

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Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa

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