F&P Math 10 - Lesson 6.5

Introduction

In this tutorial, we will explore the slope-point form of the equation for a linear function, a fundamental concept in algebra. Understanding this form not only enhances your math skills but also provides a practical tool for solving real-world problems involving linear relationships.

Step 1: Understand the Slope-Point Form

The slope-point form of a linear equation is expressed as:

y - y1 = m(x - x1)

Where:

• (x1, y1) is a point on the line.
• m represents the slope of the line.

Practical Advice

• The slope m indicates the rate of change, showing how much y changes for a unit change in x.
• Ensure you can identify a point on the line and calculate the slope before using this form.

Step 2: Identify the Slope

To find the slope of a line, use the formula:

m = (y2 - y1) / (x2 - x1)

Practical Advice

• Choose two distinct points on the line, (x1, y1) and (x2, y2).
• Be careful with the order of points; the first point should correspond to y1 and x1, while the second to y2 and x2.
• Remember that positive slopes rise from left to right, while negative slopes fall.

Step 3: Plug Values into the Slope-Point Form

Once you have the slope and a point on the line, substitute these values into the slope-point form equation.

Example

If the slope is

2

and the point is (3, 4):

y - 4 = 2(x - 3)

Practical Advice

• Simplify the equation to its slope-intercept form (y = mx + b) if needed for further analysis or graphing.

Step 4: Graph the Linear Function

To visualize the equation you've created, graph it on a coordinate plane.

Steps to Graph

1. Plot the point (3, 4) on the graph.

Use the slope to find another point

• From (3, 4), move up 2 units and right 1 unit to find the next point (4, 6).
2. Draw a line through the points (3, 4) and (4, 6).

Practical Advice

• Use a ruler for straight lines, and ensure your graph is clearly labeled.

Conclusion

In this tutorial, we covered the slope-point form of linear equations, how to identify the slope, and how to graph the linear function. Mastering these steps will enhance your understanding of linear relationships and prepare you for more advanced concepts in mathematics.

Next, practice creating your equations using different points and slopes, and try to graph them for further reinforcement of the concepts learned.