Determining the Equation of a Line Given Its Slope and a Point
In the realm of mathematics, particularly when dealing with linear equations, one of the most crucial concepts involves determining the equation of a line given its slope and a point through which it passes. This article will walk you step-by-step through the process of forming and applying the point-slope form of a linear equation. Furthermore, we will use a real-world example to illustrate this concept clearly, providing a comprehensive guide for SEO with the necessary keyword optimization for better Google search rankings.Understanding the Point-Slope Form of a Linear Equation
The point-slope form of a line is a fundamental way to express the equation of a line, especially when the slope of the line and a point on the line are known. The general form of the point-slope equation is given by:Point-Slope Equation:
For a line with slope m that passes through the point ((x_0, y_0)), the equation of the line in point-slope form is:
[y - y_0 m(x - x_0)]Example: Finding the Equation of a Line with Slope -4 and Passing Through the Point (-5, 2)
To find the equation of a line with a given slope and a point through which it passes, you can simply substitute the given values into the point-slope form. In this case, the slope (m -4) and the point ((x_0, y_0) (-5, 2)). Now, let's break down the process of determining the equation step by step.Step 1: Identify the Given Values
- Slope ((m)): -4 - Point: ((x_0, y_0) (-5, 2))Step 2: Substitute into the Point-Slope Equation
Substituting these values into the point-slope form equation gives: [y - 2 -4(x 5)]Step 3: Simplify the Equation
To express the equation in a more recognizable form, you can simplify the right-hand side of the equation: [y - 2 -4(x 5)] Distribute the -4 on the right-hand side: [y - 2 -4x - 20] Add 2 to both sides to solve for (y): [y -4x - 20 2] Simplify the constant terms: [y -4x - 18] Thus, the equation of the line is: [y -4x - 18]SEO Optimization for Better Google Search Rankings
To ensure that this article ranks well in Google searches, we need to include the primary keywords and meta descriptions that align with our content. Below is the structure of the meta description to enhance SEO performance:Learn how to form and apply the point-slope form of a linear equation when given a slope and a point. Discover the equation for a line with slope -4 passing through (-5, 2).
In this content, we have strategically placed the keywords "slope," "point-slope form," and "equation of a line" throughout the article to improve visibility in search engine results. This strategic placement of keywords and a clear, concise meta description will help the article achieve better ranking in Google. Additionally, including these keywords in headers (like H1, H2) and throughout the text will enhance the document's relevance and provide a rich user experience, which is crucial for SEO.