Your Result is copied!

ADVERTISEMENT

Determine the point slope form of a straight line equation by entering either one point (x1, y1) and slope (m), or two points (x1, y1)(x2, y2). Get complete solution with graphical view to understand the problem better.

Add this calculator to your site

ADVERTISEMENT

ADVERTISEMENT

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

**Support**

**Email us at**

© Copyrights 2024 by Calculator-Online.net