Understanding Point Slope Form: An Explanation and Example

Point Slope Form

The point slope form is a way to represent a linear equation, specifically when you know the slope of the line and a point on the line

The point slope form is a way to represent a linear equation, specifically when you know the slope of the line and a point on the line.

The point slope form is written as follows:

y – y1 = m(x – x1)

Where:
– (x1, y1) is a point on the line
– m is the slope of the line

To use the point slope form, you need to know the values of at least one point on the line and the slope. Let’s go through an example to better understand how to use it.

Example:
Find the equation of the line with slope 3 that passes through the point (2, 5).

Solution:
Given that the slope is 3 and the point is (2, 5), we can use the point slope form to find the equation of the line.

Using the point slope form equation: y – y1 = m(x – x1), we substitute the values we know.

y – 5 = 3(x – 2)

Next, we distribute the 3 on the right side:

y – 5 = 3x – 6

To isolate y, we add 5 to both sides of the equation:

y = 3x – 1

So, the equation of the line with slope 3 that passes through the point (2, 5) is y = 3x – 1.

Remember, the point slope form is a useful tool when you have a known point on a line and the slope. It allows you to quickly write the equation of the line without needing to determine the y-intercept.

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