Point Slope Form Calculator

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