Write the slope intercept form of the equation calculator

Find the slope intercept equation of a line (y=mx+b or y=mx+c) from two points with this slope intercept form calculator.

Slope Intercept Form Equation: y = mx + b, or sometimes y = mx + c,

m = slope (the amount of rise over run of the line)
b= y-axis intercept ( where the line crosses over the y-axis)

To calculate the slope intercept form equation from two coordinates
(x1,y1) and (x2,y2):

Step 1: Calculate the slope (y2 - y1) / (x2 - x1)

Step 2: Calculate where the line intersects with the y-axis by
entering one of the coordinates into this equation: y - mx = b

Example:

To calculate the slope-intercept equation for a line that includes
the two points ( 7, 4) and (1, 1).

Step 1: slope (m) = (1 - 4) / (1 - 7) = -3 / -6

slope (m) = -3/-6 = 1/2

Step 2: Using one of the original coordinates (7, 4) we find the
y-axis intercept (b) using the formula: y - mx = b

y=4, m=1/2, x =7

y - mx = b

b= .5

The slope intercept form for this line is y = .5x + .5

This line crosses the y-axis at .5 and has a slope of .5,
so this line rises one unit along the y-axis for every 2 units
it moves along the x-axis.

So, where would you ever use this? Here's an article on ways to use the Slope Intercept Form in Real Life.

The slope-intercept form calculator will find the slope of the line passing through the two given points, its y-intercept, and the slope-intercept form of the line, with steps shown.

Related calculators: Line Calculator, Slope Calculator, Parallel and Perpendicular Line Calculator

Your Input

Find the equation of a line given two points $$$P = \left(-1, 5\right)$$$ and $$$Q = \left(3, 7\right)$$$.

Solution

The slope of a line passing through two points $$$P = \left(x_{1}, y_{1}\right)$$$ and $$$Q = \left(x_{2}, y_{2}\right)$$$ is given by $$$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$$$.

We have that $$$x_{1} = -1$$$, $$$y_{1} = 5$$$, $$$x_{2} = 3$$$, and $$$y_{2} = 7$$$.

Plug the given values into the formula for a slope: $$$m = \frac{7 - 5}{3 - \left(-1\right)} = \frac{1}{2}$$$.

Now, the y-intercept is $$$b = y_{1} - m x_{1}$$$ (or $$$b = y_{2} - m x_{2}$$$, the result is the same).

$$$b = 5 - \left(\frac{1}{2}\right)\cdot \left(-1\right) = \frac{11}{2}$$$

Finally, the equation of the line can be written in the form $$$y = b + m x$$$:

$$$y = \frac{x}{2} + \frac{11}{2}$$$

Answer

The slope of the line is $$$m = \frac{1}{2} = 0.5$$$A.

The y-intercept is $$$\left(0, \frac{11}{2}\right) = \left(0, 5.5\right)$$$A.

The equation of the line in the slope-intercept form is $$$y = \frac{x}{2} + \frac{11}{2} = 0.5 x + 5.5$$$A.

An online standard form to slope intercept form calculator allows you to determine both standard form and slope form of an equation more precisely. But a direct use of this equation to slope intercept form calculator will confuse you regarding the terms involved in calculations. Let us learn about these particular conversions further.

Stay Focused!

Standard Form of An Equation:

The generic form of a linear equation is written in the format given below:

$$ A_{x} + B_{y} = C $$

Where:

• A and B and C are the coefficients
• x and y are the respective variables involved

You can convert intercept form to its corresponding standard form by using slope to standard form calculator.

Slope Intercept Form of An Equation:

You can write the equation in its intercept form as follows:

$$ y = mx + c $$

Where:

m = slope of the line
x = x-intercept
y = y-intercept

Here the transition among both of these forms may confuse you. But do not worry as our free standard to slope intercept form calculator will carry out conversions for you.

How To Convert Standard From To Slope Intercept Form And Vice Versa?

In this section, we will be solving a couple of examples for you so that you may not feel any difficulty while doing calculations. Let’s move on!

Example # 01:

Convert the following standard form of the equation into its respective slope intercept form

$$ 2x – 9y = 15 $$

Solution:

As we know that the slope intercept form of the equation is as follows:

$$ y = mx + c $$

Converting the given equation in its slope intercept form now:

$$ 2x – 9y = 15 $$

$$ -9y = -2x + 15 $$

$$ -9y = -\left(2x + 15\right) $$

$$ 9y = 2x – 15 $$

$$ y = \frac{2x – 15}{9} $$

$$ y = \frac{2x}{9} – \frac{15}{9} $$

$$ y = 0.222x -1.666 $$

Which is the required slope intercept form of the given standard equation.

Now we have:

$$ Slope = 0.222 $$

For x-intercept, we have:

$$ y = mx +c $$

Putting y = 0:

$$ 0 = mx +c $$

$$ x = -\frac{c}{m} $$

$$ x = -\frac{1.666}{0.222} $$

$$ x = 7.5 $$

$$ Y-intercept = -1.666 $$

$$ \text{Percentage Grade} = Slope * 100 $$

$$ \text{Percentage Grade} = 0.222 * 100 $$

$$ \text{Percentage Grade} = 22.22% $$

For angle, we have:

$$ \theta = arctan\left(\frac{y}{x}\right) $$

$$ \theta = arctan\left(\frac{-1.666}{7.5}\right) $$

$$ \theta = arctan\left(0.222\right) $$

$$ \theta = 12.51^\text{o} $$

As you see these computations are tricky to understand for everyone. That is why our free online standard form to slope intercept form calculator does these complex calculations automatically and displays results on your screen.

Example # 02:

Convert the following slope intercept form of the equation into its standard form:

$$ y = \frac{1}{9}x + c $$

Solution:

Here we have:

$$ y – \frac{1}{9}x – 6 = 0 $$

$$ 9y – x 54 = 0 $$

$$ -x + 9y – 54 = 0 $$

$$ x – 9y + 54 = 0 $$

$$ x – 9y = 54 $$

Which is the required standard form of the given slope intercept equation.

The slope intercept form to standard form calculator also does the same calculations but saving your precious time and generating instant results.

How Standard Form To Slope Intercept Form Calculator Works?

This free slope intercept to standard form calculator takes a time span of seconds to generate the slope intercept form accurately. Let us guide you how!

Input:

• First of all, select either you want to determine slope intercept form or standard form from the drop down list.
• Right after doing so, write down the parameters that matches the criteria of your choice
• Tap the calculate button

Output:

The equation to standard form calculator displays:

• Standard form of the equation
• Slope intercept form of the equation
• x and y intercepts
• Percentage grade
• Angle between x and y axis
• Detailed step-by-step calculations

FAQ’s:

How does slope intercept form work?

As we know that the slope intercept form is given as follows:

$$ y = mx + c $$

Now if you look at the equation above, the subscript ‘m’ represents the slope of the line and is multiplied by the x (independent variable). The constant b represents the value of the dependent variable which is y. In actual, b is a point where the line touches the vertical y-axis. This is how the slope intercept form works and helps you to draw linear standard equations.

Is slope-intercept form and point-intercept form the same?

No. A slope-intercept form is considered as the particular case of the point slope form. The point under consideration in point slope form is y. So, for converting a standard form to point slope form, you first convert it into the slope-intercept form. After that, moving b to the left side of the equation yields the point-slope form. The free standard form to slope intercept form calculator provides you with an edge of determining the azimuthal form of any equation.

What is the basic difference between slope and the intercept?

In graphical analysis, the slope of a particular line displays its steepness. While on the other hand, the intercept indicates the point where the line intersects the x-axis or y-axis. The linear relationship among the slope and the intercept gives us the average changing rate.

What is the point slope standard form?

For linear equations, the point slope in its general form is given as follows:

$$ y – y_{1} = m\left(x – x_{1}\right) $$

The purpose of this form is to find the point on the line.(which is not the y intercept).

Conclusion:

While doing graphical analysis, slope intercept form provides a technical support to draw a fair straight line. If you are interested in determining the slope intercept form of a standard linear equation, then using a free standard form to slope intercept form calculator is your best fit.

References:

From the source of Wikipedia: Linear equation, Linear function, Geometric interpretation, Equation of a line 

From the source of Khan Academy: Standard form rules, Graphing a linear equation

From the source of Lumen Learning: Equations of Lines, The Point-Slope Formula, Standard Form of a Line, Vertical and Horizontal Lines, Parallel and Perpendicular Lines

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