Finding the Equation of a Line in Slope-Intercept Form: A Comprehensive Guide

When working with linear equations in mathematics, it is crucial to understand how to find the equation of a line in slope-intercept form. This article will guide you through the process, using the points (0, 3) and (1, 10) as an example. By following these steps, you can ensure that your content is optimized for Google and other search engines.

Understanding Slope-Intercept Form

The equation of a line in slope-intercept form is given by:

y mx b, where:

m represents the slope of the line. b represents the y-intercept, the point where the line crosses the y-axis.

Steps to Find the Line Equation

Calculate the slope Determine the y-intercept Write the equation in slope-intercept form

Step 1: Calculating the Slope

The formula for calculating the slope (m) between two points ((x_1, y_1)) and ((x_2, y_2)) is:

m frac{y_2 - y_1}{x_2 - x_1}

Given the points (0, 3) and (1, 10), we can substitute these values into the formula:

[m frac{10 - 3}{1 - 0} frac{7}{1} 7]

Step 2: Determine the Y-Intercept

The y-intercept (b) is the value of (y) when (x 0). In this case, the point (0, 3) tells us that the y-intercept is 3.

Step 3: Write the Equation in Slope-Intercept Form

Now that we have calculated (m 7) and (b 3), we can write the equation of the line as:

y 7x - 3

Final Answer and Verification

The equation of the line in slope-intercept form is:

y 7x - 3

SEO Optimization for Google

When creating content for the web, it is important to follow best practices for Google SEO. This includes:

Using keywords: Make sure to include relevant keywords such as slope-intercept form and line equations naturally throughout your content. Headers and subheaders: Use H1, H2, H3 tags to structure your content and make it more readable for both users and search engines. Multimedia content: Incorporate images, diagrams, and videos to explain complex concepts visually. Quality backlinks: Ensure your content is referenced by other high-authority sites.

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Conclusion

Understanding how to find the equation of a line in slope-intercept form is a fundamental skill in algebra. By following the steps outlined in this article, you ensure that your mathematical content is both accurate and optimized for Google and other search engines. If you need further assistance, feel free to contact us!