Shortcuts in Graphing Linear Function

Shortcuts in Graphing Linear Functions

By: RICHARD R. RAQUEÑO

To graph a linear function quickly, use its slope-intercept form, y = mx + b. Plot the y-intercept, (0, b), and then use the slope, m = rise/run, to find a second point. 

A positive slope means to move up and to the right, while a negative slope means to move down and to the right. 

Connect these two points to draw the line.

Step-by-Step Graphing Using the Slope-Intercept Form

Step 1: Rewrite in slope-intercept form (y = mx + b)

If the equation isn't in y = mx + b form, rearrange it to solve for y.

Step 2: Identify the y-intercept (b).

This is the point where the line crosses the y-axis, and it's represented by the 'b' value in the equation. Plot this point on the y-axis.

Step 3: Identify the slope (m).

This is represented by the 'm' value in the equation.

Step 4: Use the slope to find another point.

• Write the slope as a fraction, if it's not already (e.g., -2 can be -2/1).
• Rise: Move vertically from the y-intercept by the amount of the numerator.
• Run: Move horizontally from the new point by the amount of the denominator.
• For example, if the slope is 1/2, from the y-intercept, move up 1 unit (rise) and then right 2 units (run)

Step 5: Draw the line.

Connect the y-intercept and the new point with a straight line, extending it in both directions to complete the graph.

Example.

Step 1: Rewrite in slope-intercept form (y = mx + b). 

For the equation y = 2x + 1. It is already in slope-intercept form.

Step 2: Identify the y-intercept (b).

b = 1, so the y-intercept is (0, 1). Plot (0, 1).

Step 3: Identify the slope (m).
m = 2, which can be written as 2/1.

Step 4: Use the slope to find another point.

From (0, 1), move up 2 units (rise) and right 1 unit (run). This gives you a second point at (1, 3).

Step 5: Draw the line.

Draw a line through (0, 1) and (1, 3).

You can watch this video to see another example of graphing a linear function using the slope-intercept form.

Calculator:

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Simple Linear Grapher (y = mx + b) by Sir Rich

Enter Equation (e.g., 2x - 3): y =