Point-slope form uses one known point and the slope to describe a line. Substitute x1, y1, and m into the formula, then expand if you need slope-intercept form y=mx+b.
⚠Note: Point-slope form requires a defined slope. Vertical lines are written as x = x1 instead.
How Point Slope Form Works
Place the known point into the formula, keep the slope as the multiplier, then expand only if another form is needed.
Known Point
The point supplies x1 and y1.
Slope
m controls the direction and steepness.
Expansion
Distribute m to convert to y=mx+b.
Verification
The original point should satisfy the equation.
💡 Example: m=3 through (2,5): y-5=3(x-2), so y=3x-1.
Applications of Point Slope Form
Line EquationsGraphingSlope ProblemsLinear Models
Frequently Asked Questions
What is a point slope form calculator?▼
It builds a line equation from one point and a slope using y-y1=m(x-x1).
What is the point slope formula?▼
The point-slope form is y-y1=m(x-x1), where (x1,y1) is a point on the line.
How do I use this calculator?▼
Enter slope m and point coordinates x1 and y1, then click Calculate.
Can point slope form handle vertical lines?▼
Vertical lines use x=x1 instead because the slope is undefined.
Where is point slope form used?▼
It is used for writing line equations quickly when slope and one point are known.
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