## point slope form

### The point-slope form is a way to represent the equation of a linear function

The point-slope form is a way to represent the equation of a linear function. It is written as:

y – y₁ = m(x – x₁)

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

The point-slope form allows us to easily find the equation of a line given a point on the line and its slope.

To use the point-slope form, you need to know the values of x₁, y₁ (coordinates of a point on the line) and m (the slope of the line). Then, you can substitute these values into the equation to find the equation of the line.

For example, let’s say we want to find the equation of a line given the point (3, 4) and a slope of 2. We can substitute these values into the point-slope form equation:

y – 4 = 2(x – 3)

Simplifying this equation, we distribute the 2 on the right side:

y – 4 = 2x – 6

Now, we can isolate y by adding 4 to both sides:

y = 2x – 2

So, the equation of the line with the given point and slope is y = 2x – 2.

The point-slope form is useful because it allows us to determine an equation quickly and efficiently when we know a point and the slope of a line. It also helps in graphing lines and understanding their properties, such as their direction and steepness.

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