Understanding the Line Equation Through Two Given Points

When you need to find the equation of a line passing through two given points, a systematic approach allows you to simplify the process and ensure accuracy. This article will guide you through the steps to find the equation of a line passing through the points 3 5/2 and 3/2 -1, with SEO-optimized content that suits Google's standards.

Step 1: Calculate the Slope

The first critical step is to calculate the slope of the line, which can be done using the formula:

M (y2 - y1) / (x2 - x1)

Substituting the Given Points

Given points are: x1, y1 3 5/2 and x2, y2 3/2 -1.

Calculating the Numerator

The numerator of the slope formula is:
y2 - y1 -1 - 5/2 -7/2

Calculating the Denominator

The denominator of the slope formula is:
x2 - x1 3/2 - 3 -3/2

Putting It All Together

Substituting these values into the slope formula, we get:
M (-7/2) / (-3/2) 7/3

Step 2: Use the Point-Slope Form to Find the Equation

The point-slope form of the line equation is:
y - y1 M(x - x1)

Using the Given Point

Using the point (3, 5/2) in the point-slope form, we get:
y - 5/2 7/3(x - 3)

Distributing the Slope

Distribute the slope to the right side of the equation:
y - 5/2 7/3x - 21/3 y - 5/2 7/3x - 7

Isolating y

To get the equation in the slope-intercept form, we add 5/2 to both sides:
y 7/3x - 7 5/2

Simplifying the Equation

Convert -7 to a fraction with a common denominator:
-7 -14/2

Adding the fractions, we get:
y 7/3x - 14/2 5/2 7/3x - 9/2

Final Equation of the Line

The equation of the line passing through the points 3 5/2 and 3/2 -1 is:
y 7/3x - 9/2

SEO Tips for Google Optimization

Optimizing for Google requires including primary keywords in a natural and helpful context. In this article, the primary keywords are 'line equation', 'slope of a line', and 'point-slope form'. Additionally, using H1, H2, and H3 tags, and integrating these keywords into headers can improve readability and SEO ranking.

It is also beneficial to include relevant images, internal linking to other relevant articles, and incorporating FAQs about finding the equation of a line to enhance user engagement.