Use the slope calculator to find out the formula of a line to use for any two given points which the line passes through. You also use the slope finder to solve for the coefficients of slope, y-intercept, and x-intercept by using the slope formulas. Let’s cover how to use this calculator, the definition of slope, and more.
How to use the slope calculator?
Although the slope formula might make you feel overwhelmed or confused, this slope calculator is the exact opposite. It’s a simple online tool you can use to solve for the slope by inputting specific values. Here are the steps to follow for this point slope calculator:
- First, enter the value of X1.
- Then enter the value of Y1.
- Next, enter the value of X2.
- Finally, enter the value of Y2.
- After entering all of the required values, this slope of a line calculator automatically generates the values you need including the Slope, Angle, Distance, and the values of Δx and Δy.
What is slope?
Before using this slope calculator or slope finder, it’s important to understand what slope is. You can mathematically describe any given line that’s in a flat plane as a relationship between the x-axis (horizontal) and the y-axis (vertical) positions of each of the points which make up the line.
You can write this relationship down as y = [something with x]. The specific form of “[something with x]” determines the type of line that you have. For instance:
- If you have y = x² + x, this means that you have a parabola which is also known as a quadratic function.
- If you have y = mx + b where both m and b represent any given numbers, this means that you have a straight line.
This slope of a line calculator only performs calculations for straight lines. But if you want to learn more about a parabola and a parabolic function, you can use online calculators and explore the quadratic formula to understand it better.
Going back to straight lines, you can recognize straight line or linear equations easily as these have no terms with exponents. For instance, you may find a y term or an x term but you will never find either a y2 or an x2 term.
Every linear formula describes straight lines and you can express them using the equation for the slope intercept form. As we stated in our previous example, you can write the formula of any given line as:
y = mx + b.
This is what’s known as the “slope intercept form.” This is a very important formula because it provides you with two significant pieces of information namely the line’s y-intercept and the slope m. Later on, you can utilize these values when you need to perform linear interpolation.
The word “slope” refers to the gradient or the inclination of any given line. It tells you how much change you can expect from y when a fixed change occurs in x. It there is a positive change, the y values increase along with the x values. If there is a negative change, the y values decrease along with the x values.
The y-intercept refers to the value of y at which the given line crosses the y-axis. To calculate for it, you should substitute x to zero in your linear equation.
How to find slope?
So, how do you find slope without using a slope calculator? For this, let’s assume that you already know the points that your given line goes through. For the first point, it has coordinates (x₁, y₁) while the second point has coordinates (x₂, y₂). In this example, you’re solving for the y-intercept and the slope.
The first step is to substitute the coordinates of both points into the equation for the slope intercept:
for the first point: y₁ = mx₁ + b
for the second point: y₂ = mx₂ + b
The next step is to subtract your first equation from a second equation:
y₂ – y₁ = m(x₂ – x₁)
For the final step, find the slope by dividing both sides of the equation by (x₂ – x₁):
m = (y₂ – y₁)/(x₂ – x₁)
After solving for the slope, you can substitute the value into the first equation or the second one. Do this to solve for the y-intercept:
y₁ = x₁(y₂ – y₁)/(x₂ – x₁) + b
b = y₁ – x₁(y₂ – y₁)/(x₂ – x₁)
How to find the slope of a line?
With this point slope calculator, you can find any given line’s equation in a slope intercept form. Just input the required values about the points which the line goes through. Of course, you can also perform the calculation manually without the use of a slope calculator. Here are the steps:
- Start by jotting down the first point’s coordinates. Let’s say that the coordinates are x₁ = 1 and y₁ = 1.
- Next, jot down the second point’s coordinates. Let’s say that the coordinates are x₂ = 2 and y₂ = 3.
- Now that you have the values, use the slope formula to calculate the slope:
m = (y₂ – y₁)/(x₂ – x₁) = (3-1)/(2-1) = 2/1 = 2.
- Going further, you can also find the y-intercept by using x₂ and y₂ rather than x₁ and y₂:
b = y₁ – m * x₁ = 1 – 2*1 = –1
- Place all of the values together so that you can come up with a linear equation’s slope intercept form:
y = 2x – 1.
What is the slope formula?
Before we move on to the slope formula, let’s re-define slope using a simple equation:
Slope = change in y
change in x
If you want to understand this better, come up with an illustration wherein you draw a line through two given points (x1,y1) and (x2,y2). Since you express the change in x as x2 – x1 and the change in y as y2 – y1, you can come up with a general slope formula:
Slope = change in y = y2 – y1
change in x x2 – x1