Mastering Point-Slope Form: Writing Equations of Straight Lines on a Coordinate Plane

Point Slope Form

Point-slope form is a method used to write the equation of a straight line on a coordinate plane

Point-slope form is a method used to write the equation of a straight line on a coordinate plane. It is especially helpful when you know the coordinates of a point on the line and the slope of the line.

The point-slope form is given by the equation:

y – y₁ = m(x – x₁)

In this equation, (x₁, y₁) represents the coordinates of a point on the line, and m represents the slope of the line.

To use the point-slope form, follow these steps:

Step 1: Determine the coordinates of a point on the line. Let’s call this point (x₁, y₁).

Step 2: Determine the slope of the line. Let’s call this value m.

Step 3: Substitute the values of x₁, y₁, and m into the point-slope form equation: y – y₁ = m(x – x₁).

Step 4: Simplify and rearrange the equation, if necessary, to get the final equation in either standard form (Ax + By = C) or slope-intercept form (y = mx + b).

Let’s work through an example to illustrate how to use the point-slope form:

Example:
Find the equation of a line passing through the point (2, 4) with a slope of 3.

Step 1: The given point is (2, 4). Let’s call these values x₁ = 2 and y₁ = 4.

Step 2: The given slope is 3. Let’s call this value m = 3.

Step 3: Substitute the values into the point-slope form equation: y – 4 = 3(x – 2).

Step 4: Simplify and rearrange the equation:
y – 4 = 3x – 6
y = 3x – 2

The final equation of the line passing through the point (2, 4) with a slope of 3 is y = 3x – 2.

It’s important to note that the point-slope form is one of several methods that can be used to write the equation of a line. Depending on the given information, other forms such as slope-intercept form or standard form may be more appropriate.

More Answers: