Slope Calculator
Use the slope calculator to find the slope of a line that passes through 2 points or solve a coordinate given m. Plus, the calculator will also solve the slopeintercept form of a line.
Find the Slope of a Line
Find Points on a Line at a Distance From Another Point
Find a Point on a Line Given it's x or y Value
Slope:
Line Graph:
Slope Intercept Form:
Point Slope Form:
Standard Form:
Angle, Distance, & Intercepts:
Angle (θ):  63.435°


Distance:  2.236

Δx:  1

Δy:  2

xIntercept:  0.5

yIntercept:  1

Steps to Find Slope
Start with the slope formula
Step One: Substitute point values in the formula
Step Two: Simplify the fraction
Step Three: Solve for slope (m)
Right:  (x_{2}, y_{2})


Left:  (x_{2}, y_{2})

Line Graph:
Slope Intercept Form:
Point Slope Form:
Standard Form:
Slope, Angle, and Intercepts:
Slope (m):  

Angle (θ):  
xIntercept:  
yIntercept: 
Steps to Find Coordinates at a Distance From a Point
Step One: Solve for the right x_{2}:
Step Two: Solve for the right y_{2}:
Step Three: Solve for the left x_{2}:
Step Four: Solve for the left y_{2}:
Line Graph:
Slope Intercept Form:
Point Slope Form:
Standard Form:
Angle, Distance, & Intercepts:
x_{2}:  

y_{2}:  
Slope (m):  
Angle (θ):  
Distance:  
Δx:  
Δy:  
xIntercept:  
yIntercept: 
Steps to Find the Missing Coordinate
Start with the slope formula
Step One: Substitute point values in the formula:
Step Two: Simplify the equation:
Step Three: Crossmultiply the fraction and solve:
On this page:
 Slope Calculator
 How to Find the Slope of a Line
 Slope Formula
 Steps to Find Slope Using the Formula
 How to Interpret Slope
 How to Find Equations of a Line Using the Slope
 How to Find SlopeIntercept Form
 How to Find PointSlope Form
 How to Find Standard Form
 How to Find the x and y Intercepts of a Line
 How to Find a Point Given 1 Point, Slope, and Distance
 How to Convert Slope to Angle
 How to Convert Angle to Slope
 How to Find the Distance Between 2 Points
 References
How to Find the Slope of a Line
Slope is a measure of the rate of incline or steepness of a line on a graph. You can find the slope of a line by comparing any 2 points on the line. A point is an x and y value of a cartesian coordinate on a grid.
Slope, expressed m, is equal to the rise between two coordinates on a line over the run, or rather, it’s the ratio of rise to run.
Rise is the vertical change of the line, or the change in altitude or elevation, and the run is the horizontal change, or the change in distance.^{[1]}
Slope Formula
You can find the slope m of a line using the following formula:^{[2]}
m = y_{2} – y_{1} / x_{2} – x_{1}
Thus, the slope m is equal to y_{2} minus y_{1}, divided by x_{2} minus x_{1}.
Steps to Find Slope Using the Formula
To find the slope of a line using this formula, you’ll need to find 2 points along a line and find their x and y values. The value of x is the horizontal distance of the point from the vertical yaxis, and y is the vertical distance of the point from the horizontal xaxis.
Then, follow three easy steps to calculate the slope.
Step One: Substitute Points in the Slope Formula
Start by replacing the y_{1}, y_{2}, x_{1}, and x_{2} values in the formula with the coordinates for the two points on the line.
Step Two: Find the Difference in x and y Coordinates
Next, solve the numerator and denominator of the slope formula using these values. The result will be the absolute value of the distance between the x values or y values of two points.
The numerator represents the change in the value of y, which is known as the delta of y, or just Δy. You can find the delta of y using the formula:
Δy = y_{2} – y_{1}
The denominator represents the change in the value of x, which is known as the delta of x, or Δx. You can find the delta of x using the formula:
Δx = x_{2} – x_{1}
Step Three: Divide the Delta of y by the Delta of x
The final step is to divide the delta of y by the delta of x to find the slope. You can do this by dividing the numerator in the slope formula by the denominator, or more simply by using a fraction to decimal calculator.
In some cases, you may want to represent the slope as a fraction or ratio. In this case, you can simplify the fraction to reduce it to its simplest form rather than converting it to a decimal.
For example, let’s find the slope of a line that passes through the points (3,2) and (11,8).
Start with the slope formula:
m = (y_{2} – y_{1}) / (x_{2} – x_{1})
Replace the x and y values with the coordinate’s x and y values.
m = 8 – 2 / 11 – 3
Solve the numerator and denominator to find the delta of x and y.
m = 8 – 2 / 11 – 3 = 6 / 8
Then, reduce the fraction to its simplest form.
m = 6 / 8 = 3 / 4
So, the slope m is equal to 3 / 4
The slope formula is useful for points along a linear line, but when working with nonlinear functions, you might need to use an average rate of change calculator.
How to Interpret Slope
While the slope of a line doesn’t tell us where the line is located on the graph, it does tell us the angle of the line.
If the slope is positive, then the line is slanted up and rises from left to right on the graph.
If the slope is negative, then the line is slanted down and drops from left to right on the graph.
If the slope is equal to zero, the line is a horizontal line and does not slant up or down. This is a line with no slope.
In the special case of a vertical line, the slope is undefined. Essentially the slope would be infinite in this case, and because this would result in the denominator of the slope formula being zero since there is no change in x, it is undefined.
How to Find Equations of a Line Using the Slope
Now that you found the slope, you can express a linear line using one of several equations. The most common equations for a line are slopeintercept form, pointslope form, and standard form.
How to Find SlopeIntercept Form
Slopeintercept form is one of the most commonly used equations to represent a linear line. You can find the equation of a line using slopeintercept form given the slope m and one point on the line.
SlopeIntercept Form Equation
The slopeintercept form equation is:^{[3]}
y = mx + b
The slopeintercept form equation states that the y value of a coordinate on the line is equal to the x value of the coordinate times the slope m, plus the yintercept b.
For example, let’s solve for b, given a slope of 1/2 and a point (5,4). We’ll express this line in slopeintercept form.
Substitute for m:
y = 1 / 2 × x + b
Substitute the point values for x and y:
4 = 1 / 2 × 5 + b
Solve for b:
4 = 2.5 + b
4 – 2.5 = b
1.5 = b
Substitute b in the equation to find the slopeintercept form:
y = 1 / 2x + 1.5
How to Find PointSlope Form
Pointslope form is another commonly used equation to represent a line. You can find the equation of a line using pointslope form given the slope m and one point on the line.
PointSlope Form Equation
The pointslope form equation is:^{[4]}
y – y_{1} = m(x – x_{1})
The pointslope form equation states that y minus the y_{1} coordinate is equal to the slope m times x minus the x_{1} coordinate.
For example, let’s express the same line from the previous example using pointslope form. Recall the line has a slope of 1/2 and a point (5,4).
Substitute for m:
y – y_{1} = 1 / 2(x – x_{1})
Substitute the point values for x and y:
y – 4 = 1 / 2(x – 5)
So, the pointslope form for this line is y – 4 = 1 / 2(x – 5).
How to Find Standard Form
Standard form is a standardized format for linear equations. To use standard form, the slope and coordinates must be whole numbers; decimal values are not supported in standard form.
Standard Form Equation
The standard form equation is:
Ax + By = C
Given either of the line equations above, you can convert to standard form by simply rearranging the equations to isolate C on one half of the equation. If there are any fractions, then multiply both sides of the equation by the denominator of the fractions to remove them.
This formula represents the standard form for linear equations, but numbers can also be expressed in standard form as well.
How to Find the x and y Intercepts of a Line
Given the slope of a line and one point on it, you can find the x and y intercepts using one of the line equations above. Start by finding the slopeintercept form equation for the line.
Then, given slopeintercept form, you can find the yintercept by setting x in the equation to 0 and solving.
And to find the xintercept, set y in the equation to 0 and solve it using algebra.
For example, let’s find the x and y intercepts of the line y = 1 / 2x + 8.
Start by setting x to 0.
y = (1 / 2 × 0) + 8
Then solve for y.
y = 8
When x is equal to zero y is equal to 8, so 8 is the yintercept.
Next, set y to 0.
0 = 1 / 2x + 8
Then solve for x.
0 = 1 / 2x + 8
0 – 8 = 1 / 2x + 8 – 8
8 = 1 / 2x
8 / 1 = 1 / 2x
8 × 2 / 1 = 1 × 2 / 2x
16 / 1 = 2 / 2x
16 = x
When y is equal to zero, x is equal to 16, so the xintercept is 16.
How to Find a Point Given 1 Point, Slope, and Distance
Points on a line can be solved given the slope of the line and the distance from another point. The formulas to find x and y of the point to the right of the point are:
x_{2} = x_{1} + d / (1 + m^{2})
y_{2} = y_{1} + m × d / (1 + m^{2})
The formulas to find x and y of the point to the left of the point are:
x_{2} = x_{1} + d / (1 + m^{2})
y_{2} = y_{1} + m × d / (1 + m^{2})
How to Convert Slope to Angle
The angle of a line in degrees can be found from the inverse tangent of the slope m.
θ = tan^{1}(m)
For example, if m = 5, then the angle in degrees is tan^{1}(5).
Our rise and run to degrees converter can help calculate the value in degrees given the rise and run of a line.
How to Convert Angle to Slope
It’s also possible to convert an angle in degrees to slop, which is equal to the tangent of the angle.
m = tan(θ)
For example, if angle = 72, then m is equal to tan(72).
How to Find the Distance Between 2 Points
The formula to find the distance d between two points on a line is:
d = √((x_{2} – x_{1})^{2} + (y_{2} – y_{1})^{2})
One realworld example of using slope is to calculate the grade for landscaping and roadwork projects.
References
 LibreTexts Mathematics, Your Guide to Intermediate Algebra  3.3: Slope Intercept Form, https://math.libretexts.org/Courses/Kansas_State_University/Your_Guide_to_Intermediate_Algebra/03%3A_Linear_Equations_and_Graphs/3.03%3A_Slope_Intercept_Form
 Marecek, L., Mathis, A., Intermediate Algebra 2e  3.2 Slope of a Line, OpenStax, https://openstax.org/books/intermediatealgebra2e/pages/32slopeofaline
 CK12 Foundation, Linear Equations in SlopeIntercept Form, https://www.ck12.org/book/ck12algebrabasic/section/5.1/
 Clapham, C., Nicholson, J., Oxford Concise Dictionary of Mathematics, 475. https://web.archive.org/web/20131029203826/http://web.cortland.edu/matresearch/OxfordDictionaryMathematics.pdf