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# Point Slope Form Calculator

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.

I Want To Calculate:

X1:

Y1

Slope (m):

X1:

Y1:

X2:

Y2:

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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 of 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

## What Is Point-Slope Form?

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.

## How To Find Point Slope Form of Equation?

### Case # 01: When One Point 7 Slope Is Given

#### Data Given:

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

#### Calculations:

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.

### Case # 02: When Two Points Are Given

#### Data Given:

$$Point_1=(2, 5)$$
$$Point_2=(6, 2)$$

#### Calculations:

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:

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

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

$$y-5-0.75x+1.5=0)$$

$$-0.75x+y-3.5=0)$$

## Faqs:

### What Is An Equation of a Straight Line?

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 $$y-axis$$.

### What Are Different Forms of Equation?

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

### How Do I Convert The Point-Slope To Slope Intercept?

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.

## References:

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

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