# Point Slope Form Calculator

The point-slope form calculator will show you how to find the equation of a line from a **point on that line** and **the line's slope**. Soon, you will know what is point-slope form equation, and learn how is it different from the slope-intercept form equation. We also came up with two exercises, and we'll explain how to solve them in the last paragraph.

## What is a slope?

Let's start with the basics. What is the slope? The slope, also known as the gradient, is the marker of a line's steepness. If it's positive, it means the line rises. If it's negative - the line decreases. If it's equal to zero, the line is horizontal.

You can find the slope between two points by estimating **rise over run** - the difference in height over a distance between two points.

So, slope formula is:

`m = change in y / change in x = (y - y₁) / (x - x₁)`

The point-slope form equation is a rearranged slope equation.

To find the gradient of non-linear functions, you can use the average rate of change calculator.

## What is the point-slope form?

There is more than one way to form an equation of a straight line. Point-slope form is a form of a linear equation, where there are three characteristic numbers - two coordinates of a point on the line, and the slope of the line. The point slope form equation is:

`y - y`

,_{1} = m * (x - x_{1})

where:

`x`

,_{1}`y`

are the coordinates of a point, and_{1}`m`

is the slope.

Do you see the similarity to the slope formula? What you might not know is that it's not the only way to form a line equation. The more popular is the slope intercept form:

`y = m * x + b`

,

where:

`m`

is the slope; and`b`

is the intercept of the y-axis.

The truth is that this is nothing else than a more precise point-slope form. A straight line intercepts the y-axis in a point (0, b). If you choose this point - (0, b), as a point that you want to use in the point-slope form of the equation, you will get:

`y - b = m * (x - 0)`

, which is the same as `y = m * x + b`

.

In the two graphs below, you can see the same function, only described with two different forms of a linear equation:

## How to find the equation of a line with slope and coordinates of a point?

Let's have a look at two exercises, to understand the topic more clearly.

The slope of a line is 2. It passes through point A(2, -3). What is the general equation of the line?

- Identify the point coordinates:
`x`

,_{1}= 2`y`

._{1}= -3

- Identify the slope:
`m = 2`

- Input the values into the point slope form formula:
`y - y`

_{1}= m (x - x_{1})`y - (-3) = 2(x - 2)`

- Simplify to get the general equation:
`y = 2x - 4 -3`

`0 = 2x - y - 7`

Let's solve an exercise with a more relatable subject.

Let's say you got a puppy. When you got him he was 14 pounds. It grew 0.2 pounds every day, and after 30 days, he was 20 pounds. Find the general equation of the puppy's growth.

- The slope is the change of weight per day:
`m = 0.2`

- The characteristic point is 20 pounds on 30th day:
`(x`

_{1}, y_{1}) = (30, 20) - Now, input the values into the point-slope formula:

`y - 20 = 0.2 * (x - 30)`

4. Simplify the equation to get the general equation:

`0 = 0.2x - y + 14`

💡 If you need to find a different point on your line click on the `advanced mode` button. Then, input one coordinate, and get the other. |

And here you have it! We hope you enjoyed our point-slope form calculator! Before you go, check out more of our

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