Question

Make a table and a graph of y = 4x + 2.

Answer 1

Sure! Let's create a table of values for the equation \( y = 4x + 2 \) over a range of \( x \) values, and then I'll describe how to plot it on a graph.

### Table of Values

| \( x \) | \( y = 4x + 2 \) |
|---------|-------------------|
| -2 | -6 |
| -1 | -2 |
| 0 | 2 |
| 1 | 6 |
| 2 | 10 |
| 3 | 14 |

### Plotting the Graph

1. **Coordinate Points**: Plot the points from the table on a Cartesian coordinate system:
- (-2, -6)
- (-1, -2)
- (0, 2)
- (1, 6)
- (2, 10)
- (3, 14)

2. **Draw the Line**: Connect these points with a straight line, as the equation represents a linear function.

3. **Label Axes**: Make sure to label the x-axis and y-axis appropriately.

### Description of the Graph

- The line will have a positive slope of 4, indicating that for every 1 unit increase in \( x \), \( y \) increases by 4 units.
- The y-intercept (where \( x = 0 \)) is 2, meaning the line crosses the y-axis at the point (0, 2).

If you want to plot this graph physically, you can use graph paper or software that allows you to create graphs, like Desmos or any other graphing tool.