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# Point Slope Form Calculator

Enter the values of X_{1, }Y_{1, }and (m) in the below input boxes and hit the ** Calculate** button to get the equation of a straight line using point slope form calculator.

**Point Slope form Calculator**

Point slope calculator** **is an online tool developed to find the equation of a straight line using the slope and point on that line or two points.

**What is point-slope?**

Point slope form is a general form for linear equations. The equation of a line can be determined by using the point-slope form or slope intercept form. The point slope form highlights the slope of the line and a point on the line.

The slope of the line is the ratio of the change in the values of the y-axis and the change in the values of the x-axis [`(y`

]. It is used to evaluate the steepness of the line. _{2} – y_{1})/(x_{2} – x_{1})

You can find the equation of point-slope form in the below section.

**Point slope formula**

The point slope equation can be expressed as:

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

Where,

is the slope, and*m*

are the coordinates of a point.*x*_{1}*,**y*_{1}

**How to find the equation of a line?**

To find the equation of a straight line without a point slope form calculator,** **follow the below examples.

*Example 1: For 1 point & slope*

Find the equation of a line whose known points are

and the slope of line is *(2, 3)**8.*

*Solution:*

**Step 1: **Identify and write down the values.

x_{1 }= 2

y_{1 }= 3

`m = 8`

**Step 2: **Place the values in the point slope formula and solve the equation.

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

`y – 3 = 8(x - 2)`

Further simplification

y – 3 = 8x – 16

8x – 16 – y + 3 = 0

8x – 13 – y = 0

`y = 8x – 13`

*Example 2: For 2 points *

Evaluate the linear equation of the line whose coordinate points are `(10, 15)`

and `(12, 20)`

*Solution:*

**Step 1: **Write the given points of the line.

x1 = 10

x2 = 12

y1 = 15

y2 = 20

**Step 2: **Evaluate the slope of the line.

m = (y_{2} – y_{1})/(x_{2} – x_{1})

m = (20 - 15)/(12 - 10)

`m = 5/2 = 2.5`

**Step 3: **Now place the slope and 1 point of the line to the point-slope equation.

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

`y - 15 = 2.5(x - 10)`

Further simplification

y - 15 = 2.5x - 25

y = 2.5x - 25 + 15

`y = 2.5x - 10`

## FAQs

**How to convert slope intercept form to point slope form?**

Below are the steps to convert `y=mx+c`

to `y−y`

:_{1}=m(x − x_{1})

**Determine****the Slope and Y-intercept**: From the equation`y=mx+c`

, determine the values of slope “**m**” and**y-intercept (c)**.**Use the Y-intercept as the Point**: In the slope-intercept form, you always have a known point on the line: the y-intercept`(0, c)`

. You can use this point to write the equation in point-slope form.**Input values into Point-Slope Formula**: Use the y-intercept`(0, c)`

as your`x`

in the point-slope formula._{1},y_{1}`y−y`

_{1}=m(x−x_{1})

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

To find the equation of a line given a slope “`m`

” and a point `(x`

, you can use the point-slope form of a linear equation:_{1}, y_{1})

Let's explore how to use it:

**Input****the given values**: Insert the known values for the slope “**m**” and the point**(x**into the point-slope formula._{1}, y_{1})**Simplify the equation**(optional): You can rearrange the equation to get it in slope-intercept form`y=mx+c`

or standard form`Ax+By=C`

, depending on your preference or the requirements of your task.

**Example**:

Given the point `(2, 3)`

and a slope `m = 4`

, let's find the equation of the line.

**Solution**

**Input**** the values**:

Using the point-slope form: y−3=4(x − 2)

**simplify**:

y−3=4x−8

y=4x−5

So, the equation of the line in slope-intercept form is `y = 4x − 5`

.

**How to convert the point-slope form to the standard form Ax+By=C?**

Follow the below steps:

- Start with the point-slope form:
`y − y`

._{1}_{ }= m(x − x_{1}) - Distribute the right side:
`y − y`

._{1}_{ }= mx − mx_{1} - Rearrange the terms to get the equation in the form
`Ax + By = C`

If “**m**” is a fraction, multiply every term by the denominator to eliminate fractions.

**How to graph the line from the point and the slope?**

Follow these steps:

- Plot the given point
`(x`

on the graph._{1}, y_{1}) - From this point, use the slope to determine a second point:

- Rise = Numerator of the slope
- Run = Denominator of the slope

For example, if the slope **m = 2/3**, rise **2** units up and run **3** units to the right to find your second point.

- Draw a straight line through the two points. Extend the line in both directions.

**How to convert the point-slope form to the slope-intercept form y=mx+b?**

Follow the below steps:

- Begin with the point-slope form:
`y − y`

._{1}=m(x − x_{1}) - Solve for y by rearranging the terms:
`y = mx − mx`

._{1}_{ }+ y_{1} - The equation will now be in the form
`y = mx + c`

, where**c**is the y-intercept.