The equation of a linear function can be written in general form as ax + by = c, where a, b, and c are constants. Or in the slope-intercept form, y = mx + c. Graphs are created by setting up a table.

To graph a linear function, you can start by choosing a few values for x and then plugging them into the equation to find the corresponding y values. Once you have a few points, you can plot them on a coordinate plane and connect them with a straight line.

For example, let's say we have the linear function y = 2x + 3. We can choose a few values for x, such as x = -2, -1, 0, 1, and 2, and then plug them into the equation to find the corresponding y values:

When x = -2, y = 2(-2) + 3 = -1
When x = -1, y = 2(-1) + 3 = 1
When x = 0, y = 2(0) + 3 = 3
When x = 1, y = 2(1) + 3 = 5
When x = 2, y = 2(2) + 3 = 7

Now we can plot these points on a coordinate plane and connect them with a straight line to graph the linear function y = 2x + 3. The resulting graph will be a straight line with a slope of 2 and a y-intercept of 3.

General Form of a Linear Function:

- ax + by = c

where:

- a, b, and c are constants

Slope-Intercept Form:

- y = mx + c

where:

- m is the slope of the line
- c is the y-intercept (where the line crosses the y-axis)

Creating Graphs Using a Table:

1. Choose a range of values for the independent variable (x).
2. Substitute each x-value into the equation to solve for the corresponding y-value.
3. Create a table with the x and y values.
4. Plot the points from the table on a coordinate plane.
5. Connect the points with a straight line.