Table of Contents

*Point slope form calculator*

*Point slope form calculator*

*The formula of point-slope form calculator is used to find the equation of a Straight line.*

Table of Contents

*The formula of point-slope form calculator is used to find the equation of a Straight line.*

Point Slope Form Calculator

NOTE :-If your slope is fraction, please convert in to decimal, then enter the slope in the box provided.

Example : 1/2 to be entered as 0.5

**The procedure to use the point-slope form calculator is as below:**

**Step 1:** Enter the values of X1,Y1 & M slope in the value box.

**Step 2:** Click on Calculate button in the middle of the calculator.

**Step 3:** Check below value box for the equation of the line.

**There are some other different forms of the equation of a straight line.**

- Point-Slope Form calculator
- Slope Intercept Form
- Two points form.
- Intercept form

**Coordinate Geometry Calculators **

Slope Form Calculator | Slope Intercept Form Calculator |

Triangle Area Calculator | Centroid Triangle Calculator |

Perpendicular Bisector Calculator | Mid Point Calculator |

Distance Between Two Points Calculator |

This formula is used only when we know the slope of the straight line and a point on the straight line.

The equation of a straight line whose slope is m and which passes through a point (x1, y1) is found using the point slope form.

The equation of the point-slope formula is:

y – y1 = m ( x – x1) |

The equation for the slope of a straight line is:

y – y1 = m ( x – x1) |

Equation Description | Derivation method |
---|---|

The equation for the slope of a straight line is | Slope\;m=\frac{Diff.\;in\;y\;-\;coordinate}{Diff.\;in\;x\;-\;coordinate} |

Now the Equation is : | m=\frac{y\;-\;y1\;}{x-\;x1} |

Multiplying both sides by (x−x1) | m\;(x\;-\;x1)\;=\;y-\;y1 |

This can be written as, | y-\;y1\;=\;\;m\;(x\;-\;x1) |

where,

- (x, y) is a random point on the straight line used as variables while applying the formula.
- m is the slope of the straight line.
- (x1,y1) is a fixed point on the straight line.

The equation is useful only when we have:

- one point on the line:
_{1},y_{1}) - and the Slope of the line: m,

Hence the point-slope formula is proved.

Slope-intercept form calculator is the commonly used form for the equation of a line and is derived as,

y = mx + b |

Equation Description | Derivation method |
---|---|

The Point-Slope Form equation is | y-\;y1\;=\;\;m\;(x\;-\;x1) |

(x1 , y1) is actually (0 , b) | y\;-\;b\;=\;m\;(x\;-\;0) |

That is | y\;-\;b\;=\;m\;x |

Put b on another side | y\;=\;m\;x\;+\;b |

where,

- m is the slope.
- b is the value called the y-intercept.
- point (x
_{1}, y_{1}) is actually at (0, b).

It is same as point-slope form except that this equation involves the slope of a line and its y-intercept , rather than the slope of a line and a point on the line.

It is the advance case of point-slope form shows that the Point on the line is also the y-intercept.

Because of the slope and y-intercept, it is easy to write the equation of a line in slope-intercept form, and also to graph it.

Hence the slope-Intercept form is proved.

Intercept form equation of a line is one of the method to find the equation of a line.

Here, we will find the equation of a straight line by using x- intercept and y - intercept.

The Intercept Form is expressed as,

\frac{x}{a}+\frac{y}{b}=1 |

Equation Description | Derivation method |
---|---|

The Intercept Form equation is | \frac{x}{a}+\frac{y}{b}=1 |

Where,

- x- intercept = a
- y- intercept = b

**Example 1 : **

**Question : -** (x1, y1) = (2, 1) And m = 5

**Answer** **:-**

Description | Solved Equation |
---|---|

The slope of the line l is | y - y1 = m (x - x1) |

Put values as mentioned in the question. Now the equation will be : | y - 1 = 5 (x - 2) |

Now multiply 5 by x-2 | (y-1)=5(x-2) |

Which can be specified as: | y=5x-10+1 y=5x-9 |

Final Equation | 5x-y-9=0 |

**Example 2 :**

**Question : - **(x1, y1) = (2, 4) And m = 6

**Answer** **:-**

Description | Solved Equation |
---|---|

The slope of the line l is | y - y1 = m (x - x1) |

Put values as mentioned in the question. Now the equation will be : | y - 4 = 5 (x - 2) |

Now multiply 5 by x - 2 | y - 4 = 5x - 12 |

Which can be specified as: | y=5x -10 + 4 y = 5x - 6 |

Final Equation | 5x-y-6=0 |

**Example 3 :**

You can calculate the slope-intercept equation online by slope intercept calculator

You can calculate the point-slope equation online by point slope calculator

**The **equation is y-y₁=m(x-x₁) for linear equations.

The linear equation of slope-intercept form is y = mx + b.