(-6 6) (6 2) Slope Intercept Form

Suzhoumeite

4 min read

·

Jul 03, 2024

33

Share

Slope Intercept Form: Understanding the Concept with Examples

In this article, we will delve into the concept of slope intercept form, a fundamental idea in algebra and graphing. We will use the examples (-6, 6) and (6, 2) to illustrate the concept and provide a clear understanding of slope intercept form.

What is Slope Intercept Form?

The slope intercept form is a way of expressing a linear equation in the form of y = mx + b, where:

• m represents the slope of the line (how steep it is)
• b represents the y-intercept (the point where the line crosses the y-axis)

Example 1: (-6, 6)

Let's consider the point (-6, 6) and find the slope intercept form of the line that passes through this point.

To find the slope, we need another point on the line. Let's assume the other point is (0, 0), which is the origin.

Using the formula for slope m = (y2 - y1) / (x2 - x1), we can calculate the slope as:

m = (6 - 0) / (-6 - 0) = -1

Now, we can use the point-slope form y - y1 = m(x - x1) to find the equation of the line:

y - 6 = -1(x + 6)

Simplifying the equation, we get:

y = -x - 6

This is the slope intercept form of the line that passes through the point (-6, 6).

Example 2: (6, 2)

Let's consider the point (6, 2) and find the slope intercept form of the line that passes through this point.

Again, we need another point on the line. Let's assume the other point is (0, 0), which is the origin.

Using the formula for slope m = (y2 - y1) / (x2 - x1), we can calculate the slope as:

m = (2 - 0) / (6 - 0) = 1/3

Now, we can use the point-slope form y - y1 = m(x - x1) to find the equation of the line:

y - 2 = 1/3(x - 6)

Simplifying the equation, we get:

y = 1/3x - 2

This is the slope intercept form of the line that passes through the point (6, 2).

Conclusion

In conclusion, the slope intercept form is a useful way to express linear equations, and it can be easily derived from a given point on the line. By understanding the slope intercept form, we can graph lines and identify their properties, such as the slope and y-intercept.

In the examples above, we saw how to find the slope intercept form of lines that pass through specific points. This skill is essential in algebra and graphing, and it has many practical applications in real-world problems.