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**Table of Content**

Point slope form calculator functions to calculate the equation of a line from a point and its slope.

Enter the coordinates of the points and get step by step solution with the help of the graphical interpretation to determine the point-slope equation of the straight line.

**Slope is the measure of the steepness of a line. It tells you rise over run ratio of a straight line on a graph.**

- Slope intercept of a line represented by the symbol
**m** - If the slope equation of a line is positive, the graph is a straight rising line
- If the slope equation of a line is negative, the graph is a straight downward line

Point-slope form of a linear equation is it particular notation and is used to express the equation of a line in point-slope to standard form.

It is written in the form of below formula:

\(y-y_1)=m(x-x_1)\)

Where, m is the point-slope and \(x_1\) and \(y_1\) are the coordinates of the point lying on the line.

- \(\text{Coordinates of points} = (2, 5)\)
- \(Point-Slope = m = 2\)

**Step 1:** Write down the values

\(m=2\)

\(x_1=2\)

\(y_1=5\)

**Step 2:** Point-slope-intercept form formula

\(y-y_1)=m(x-x_1)\)

**Step 3:** Perform Calculations

Put values in point-slope-intercept form formula:

\((y-5)=2(x-2)\)

\((y-5)=2x-4\)

\(0=2x-4-y+5\)

\(2x-4-y+5=0\)

\(2x-y+1=0\)

Which is the required point slope equation of a line with point and slope given.

\(Point_1=(2, 5)\)

\(Point_2=(6, 2)\)

**Step 1:** Write the Coordinates

\(x_1=2\)

\(x_2=6\)

\(y_1=5\)

\(y_2=2\)

**Step 2:** Determine The Point-Slope

\(Slope=m=\dfrac{y_2-y_1}{x_2-x_1}\)

\(Slope=m=\dfrac{2-5}{6-2}\)

\(Slope=m=\dfrac{-3}{4}\)

\(Slope=m=0.75\)

**Step 3:** Determine The Point Slope Form

Using the point-slope formula:

\((y-y_1)=m(x-x_1)\)

\((y-5)=0.75(x-2)\)

\(y-5-0.75x+1.5=0)\)

\(-0.75x+y-3.5=0)\)

The equation of any straight line called the linear equation and it is written as below formula,

\(y=mx+b\)

Here,

- \(m\) is the slope of the line.
- \(b\) is the \(y-intercept\) of the line. It is the point where a line crosses the \(y-axis\).

**Standard Form:**\(Ax+By=C\)**Point Slope Form: \**((y-y_1)=m(x-x_1)\)**Slope-Intercept Form:**\(y=mx+c\)

To convert the point-slope equation, follow the below steps;

**Step 1:** Write equation in point slope form and y-intercept:

**y – b = m(x – a)**

Where;

- m _ Slope with one point
- a _ Y-intercept
- b _ X-intercept

**Step 2:** Now multiply m with coordinates inside bracket:

**y – b = mx – ma**

**Step 3:** Make addition of y-intercept on both the sides

**y = mx – ma + b**

Which is the converted slope-intercept form of the equation.

From the source of khanacademy: Intro to point-slope form

From the source of studypug: How to use point-slope form in linear equations