Write Equation in Point Slope Form

Algebra-1

1. Fundamental Concepts

Definition: The point-slope form of a linear equation is given by , where is the slope and is a point on the line.
Slope: The slope represents the rate of change of with respect to .
Point: Any point that lies on the line can be used in the formula.

2. Key Concepts

Basic Rule:

Slope Calculation: The slope can be calculated using two points and as

Application: Used to write the equation of a line when the slope and a point are known

3. Examples

Example 1 (Basic)

Problem: Write the equation of the line with slope passing through the point .

Step-by-Step Solution:

Substitute , , and into the point-slope form:
Simplify the equation:
Rearrange to get the equation in slope-intercept form:

Validation: Substitute → Original: ; Simplified: ✓

Example 2 (Intermediate)

Problem: Write the equation of the line passing through the points and .

Step-by-Step Solution:

Calculate the slope :
Use the point-slope form with either point. Using :
Simplify the equation:
Rearrange to get the equation in slope-intercept form:

Validation: Substitute → Original: ; Simplified: ✓

4. Problem-Solving Techniques

Visual Strategy: Plot the points and draw the line to visualize the slope and intercepts.
Error-Proofing: Double-check calculations for slope and substitution into the point-slope form.
Concept Reinforcement: Practice converting between different forms of linear equations.