Slope Calculator

What is slope

The slope (m) of a line is used to explain the direction and the steepness of the line. It can be calculated by two coordinates in the Cartesian coordinate system. The value can be zero, positive, negative and undefined.

Formula

\[\text{Slope}=\frac{y_2-y_1}{x_2-x_1}\]There are 3 ways to describe the linear equations with slope.
1. Slope Intercept Form\[y=mx + b\]where b is the intercept of the line and y-axis. For instance, assume the slope is 10 and the intercept is 7. A equation would become y = 10x + 7. Please note that if b is zero, the line passes through x-axis and y-axis at (0, 0).

2. Point Slope Form\[y - y_c = m(x-x_c)\]This form in fact is another form of slope intercept form. Given a coordinate A (2, 7) and slope is 12, this equation would become y - 7 = 12(x - 2). If we simplify this equation, we will get y = 12x - 17, which is same as point slope form. And from this result, we know this line passes through y-axis at (0, -17).

3. Standard Form\[Ax + By + C = 0\]This form basically rearrange the elements in slope intercept form as this form could benefit some matrix calculations.

How to find slope

• Calculate the (a) difference between two y coordinates, y2 - y1
• Calculate the (b) difference between two x coordinates, x2 - x1
• Divide the value of (a) by (b), (a) / (b)
• Check the result with this calculator