Equation of a Line from Point and Slope: Your Guide to y = mx + b
ByMuhammad Ali•Founder of KruskalCode
22:13
6 min read
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).
Explanation
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.
Formula
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.
Example
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.
How to use the related calculator
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.
Try the related calculator
Open toolFAQ
Why is y = mx + b called slope-intercept form?
It's called slope-intercept form because 'm' directly represents the slope of the line, and 'b' directly represents the y-intercept (the point where the line crosses the y-axis). This form makes it easy to visualize and graph the line.
What if the slope is zero?
If the slope (m) is zero, the line is horizontal. The equation will simplify to y = b, where 'b' is the y-coordinate of every point on the line. Our calculator handles this case correctly.
Can I use this for parallel or perpendicular lines?
Yes! If you know a line is parallel to another, it shares the same slope. If it's perpendicular, its slope is the negative reciprocal of the other line's slope. You can calculate the new slope and then use this tool.
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About the author
Muhammad Ali. Muhammad Ali is a full-stack developer and founder of KruskalCode. He builds SaaS platforms and automation systems with React and Laravel, and helps teams ship fast, scalable tools.
Need a custom calculator, dashboard, or automation workflow? Reach out to KruskalCode.
