Point Slope Form Calculator
The pointslope 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 pointslope form equation, and learn how is it different from the slopeintercept form equation. We also came up with two exercises, and we'll explain how to solve them in the last paragraph.
Let's start with the basics and discuss what the slope is.
What is a 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 pointslope form equation is a rearranged slope equation.
To find the gradient of nonlinear functions, you can use the average rate of change calculator.
🙋 For more information go to the slope calculator.
What is the pointslope form?
There is more than one way to form an equation of a straight line. Pointslope 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:
where:
 $\small x_1, x_2$ are the coordinates of a point, and
 $\small m$ 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:
where:
 $\small m$ is the slope; and
 $\small b$ is the intercept of the yaxis.
The truth is that this is nothing else than a more precise pointslope form. A straight line intercepts the yaxis in a point (0, b). If you choose this point  (0, b), as a point that you want to use in the pointslope form of the equation, you will get:
$\small y  b = m \cdot (x  0)$, which is the same as $\small y = m \cdot x + b$.
In the two graphs below, you can see the same function, only described with two different forms of a linear equation:
To learn how to find the xintercept and yintercept of a line, visit our x and yintercept calculator.
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 pointslope form formula:
 $\small y  y_1 = m (x  x_1)$
 $\small y  (3) = 2(x  2)$
 Simplify to get the general equation:
 $\small y = 2x  4 3$
 $\small 0 = 2x  y  7$
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 pointslope formula:
$\small y  20 = 0.2 \times (x  30)$

Simplify the equation to get the general equation:
$\small 0 = 0.2x  y + 14$
💡 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 pointslope form calculator! Before you go, check out more of our
!FAQ
How do I convert pointslope to slope intercept?
If you are given a pointslope form of a line, you can get the slope intercept by following these steps:
 Write down your pointslope form
y  b = m(x  a)
.  Expand the righthand side:
y  b = mx  ma
.  Add
b
to both sides:y = mx  ma + b
.  This is slopeintercept form! The slope is
m
, and the intercept isma + b
.
How do I calculate the intercept given pointslope form?
The yintercept of a line with pointslope form y  b = m(x  a)
is given by the formula intercept =
b  ma. For instance, for the line
y  1 = 2(x  3)you get the intercept
1  6 = 5`.
What is the point slope formula with zero slope?
If the slope is zero, the pointslope formula reduces to y  b = 0
. This equation describes a horizontal line that crosses the vertical axis at y = b
.
Can pointslope form be the same as the slope intercept form?
Yes! Take the line with slope intercept form y = mx + b
. Let us write down its pointslope form for the point (0, b)
. We get y  b = m(x  0)
, which is the same (up to the trivial transformation of moving b
to the righthand side) as the slopeintercept form.