The slope intercept form calculator tells you how to find the equation of a line for any given two points that this line passes through. It will help you find the coefficients of slope and y-intercept, as well as the x-intercept, using the slope intercept formulas. Read on to learn what is the slope intercept form of a linear equation.
Linear equations, or straight line equations, can be recognized by having no terms with exponents on them. (For example, you will find an x or a y, but never an x².) Each linear equation describes a straight line.
You can present the equation of any line in the form of
y = mx + b. This is the so-called slope intercept form, because it gives you two important informations: about the slope m and the y-intercept b of the line. You can use these values for linear interpolation later.
Slope is the inclination, or gradient, of a line. If it is positive, the values of y increase with increasing x; if it is negative, y decreases with an increasing x. You can read more about it in the description of our slope calculator.
Y-intercept is the value of y at which the line crosses the y-axis. To find it, you have to substitute an x = 0 to the linear equation.
How to find the slope intercept form of a linear equation, then? We will assume you know two points that the straight line goes through. The first one will have coordinates (x₁, y₁) and the second one (x₂, y₂). Your unknowns are the slope m and the y-intercept b.
Firstly, substitute the coordinates of the two points into the slope intercept equation:
y₁ = mx₁ + b
y₂ = mx₂ + b
Then, subtract the first equation from the second:
y₂ - y₁ = m(x₂ - x₁)
Finally, divide both sides of the equation by
(x₂ - x₁) to find the slope:
m = (y₂ - y₁)/(x₂ - x₁)
Once you have found the slope, you can substitute it into the first or second equation to find the y-intercept:
y₁ = x₁(y₂ - y₁)/(x₂ - x₁) + b
b = y₁ - x₁(y₂ - y₁)/(x₂ - x₁)
This slope intercept form calculator allows you to find the equation of a line in the slope intercept form, if all you have given are two points that the line goes through. You need to follow the procedure outlined below.
m = (y₂ - y₁)/(x₂ - x₁) = (3-1)/(2-1) = 2/1 = 2.
b = y₁ - m * x₁ = 1 - 2*1 = -1. You can also use x₂ and y₂ instead of x₁ and y₂ here.
y = 2x - 1.
You can also find the x-intercept of the line. It is the value of x at which the straight line crosses the x-axis (it means the value of x for which y = 0). You can calculate it in the following way:
0 = mx + b
x = -b/m
Our slope intercept calculator will display the values of x-intercept and y-intercept for you.