This calculator helps you find the equation of a straight line when you know one point on the line and its slope. It will output the equation in the familiar slope-intercept form: y = mx + b.
Enter the x-value of the known point.
Enter the y-value of the known point.
Enter the slope of the line.
This calculator helps you find the equation of a straight line when you know one point on the line and its slope. It will output the equation in the familiar slope-intercept form: y = mx + b.
The point-slope form of a linear equation is y - y₁ = m(x - x₁), where (x₁, y₁) is a known point and m is the slope. To convert this to slope-intercept form (y = mx + b), you rearrange the equation to solve for y.
Given a point (3, 5) and a slope of 2. We use y - y₁ = m(x - x₁). So, y - 5 = 2(x - 3). Distribute the slope: y - 5 = 2x - 6. Add 5 to both sides: y = 2x - 1. Here, m = 2 and b = -1.
The point-slope form is y - y₁ = m(x - x₁), where 'm' is the slope and (x₁, y₁) is a specific point on the line. It's a handy way to write a linear equation if you have these two pieces of information.
Once you have the point-slope form, simply distribute the slope 'm' on the right side, then isolate 'y' by moving the y₁ term to the right side of the equation. This will give you y = mx + b.
Yes, absolutely! This calculator is designed to work with both positive and negative values for the slope and the x and y coordinates of your point. Just enter them as usual.
Equation of a Line from Point and Slope: Your Guide to y = mx + b
Understanding how to find the equation of a straight line is a core skill in algebra. Often, you're given a point that the line passes through and its slope. This guide will walk you through the process, from the point-slope form to the more familiar slope-intercept form (y = mx + b).
A straight line can be uniquely defined by a single point it passes through and its slope. The point-slope form, y - y₁ = m(x - x₁), is a direct way to express this relationship. Here, 'm' is the slope, and (x₁, y₁) represents the coordinates of the known point. By rearranging this equation, you can easily get the line into the slope-intercept form, which clearly shows the slope and y-intercept.
The Point-Slope Form: y - y₁ = m(x - x₁) Where: • (x₁, y₁) is a known point on the line • m is the slope of the line To convert to Slope-Intercept Form (y = mx + b): 1. Distribute 'm' into (x - x₁). 2. Add y₁ to both sides of the equation.
Let's say you have a line that passes through the point (2, 7) and has a slope of 3. Using the point-slope form: y - 7 = 3(x - 2). First, distribute the 3: y - 7 = 3x - 6. Then, add 7 to both sides to isolate y: y = 3x + 1. This is the equation in slope-intercept form.
Our Equation of a Line (Point-Slope) Calculator makes this process simple. Just enter the x-coordinate of your known point into the 'Point X-coordinate (x₁)' field, the y-coordinate into 'Point Y-coordinate (y₁)', and the slope into the 'Slope (m)' field. The calculator will instantly display the equation of your line in the y = mx + b format, along with the calculated slope and y-intercept.
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