Point-Slope Form: Finding the Equation of a Line Given a Point and Slope

Point Slope Form

The point-slope form is a way of representing a linear equation in two variables, usually denoted as (x, y)

The point-slope form is a way of representing a linear equation in two variables, usually denoted as (x, y). It allows us to express the equation of a line using a single point on the line and its slope.

The point-slope form of a linear equation is given by:

y – y₁ = m(x – x₁)

where (x₁, y₁) is a point on the line, and m is the slope of the line.

To use the point-slope form, you need to have a point on the line and the slope of the line. Once you have these values, you can substitute them into the equation to find the equation of the line.

Let’s understand how to use the point-slope form with an example:

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

Using the point-slope form, we have:

y – 4 = 2(x – 3)

Now, we can simplify the equation:

y – 4 = 2x – 6

To get the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we can rearrange the equation:

y = 2x – 6 + 4

y = 2x – 2

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

By using the point-slope form, we can easily calculate the equation of a line given a point and its slope. This form is particularly useful when you have these two pieces of information and want to find the equation.

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