How to Use this slope calculator with steps

Use this calculator to find the slope of a line that you provide, with all the steps shown.

The slope is a measure of the inclination of the line with respect to the coordinated axes. A positive slope indicates that the line has a upward inclination, whereas a negative slope indicates that the line has a downward inclination.

A slope equal to zero indicates that the line is horizonal, whereas a vertical line does not have a well defined slope.

Slope Calculator from Equation

This calculator will show you how to compute the slope of a line you provide, and you will have different ways to indicate and define your line.

For example, one common way is to define your line giving an equation, and then you will have this calculator to compute the slope from the equation.

The general strategy for that is to put the equation of the line in slope-intercept form, from which point is easy to recognize the slope from the structure of the equation \(y = mx + n\).

This is a slope from two points calculator too.

Perhaps one of the most common ways to compute the slope is when you define the equation by providing two points as\((x_1, y_1)\), \((x_2, y_2)\), where the slope is computed as

\[m = \frac{y_2-y_1}{x_2-x_1}\]

which is how to find the slope from two points.

Ultimately, how to find the slope of a line will depend on how the line is defined. This calculator will get you covered with all the cases, even when there are fractions in the calculation.

Example: Calculation of the slope

Suppose that you have a line that has the following standard form \( \frac{3}{4} x + 2y = 6\). Find slope of the line.

Solution: Calculation of the Slope of a line

We have been provided with the following equation:

\[\displaystyle \frac{3}{4}x+2y=6\]

Putting \(y\) on the left hand side and \(x\) and the constant on the right hand side we get

\[\displaystyle 2y = -\frac{3}{4}x +6\]

Now, solving for \(y\), by dividing both sides of the equation by \(2\), the following is obtained

\[\displaystyle y=-\frac{\frac{3}{4}}{2}x+\frac{6}{2}\]

and simplifying we finally get the following

\[\displaystyle y=-\frac{3}{8}x+3\]

Conclusion: Based on the data provided, we conclude that the slope of the line is \(\displaystyle m = -\frac{3}{8}\).

Example: Calculation of Slope from two points

Suppose that you have a line that has passes through 2 points: \( (1, 2)\) and \( (4, 11/3)\). Find slope of the line.

Solution:

Calculation of the Slope of a line

The information provided about the line is that the line passes through the points\(\displaystyle \left( 1, 2\right)\) and \(\displaystyle \left( 4, \frac{11}{3}\right)\)

Therefore, the first step consists in computing the slope. The formula for the slope is: \[\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} \]

Now, by plugging the corresponding numbers is , we get that the slope is: \[\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{ \displaystyle \frac{11}{3} - 2}{ \displaystyle 4 - 1} = \frac{ \displaystyle \frac{11}{3}-2}{ \displaystyle 4-1} = \frac{5}{9}\]

So then, we find that the slope is \(\displaystyle m = \frac{5}{9}\) and that the line passes through the point \(\displaystyle \left( 1, 2\right)\)

Conclusion: Based on the data provided, we conclude that the slope of the line is \(\displaystyle m = \frac{5}{9}\).

The slope of a line is one of its most important properties, along with the y-intercept and x-intercept, because they essentially define the line.