Point-Slope Y Calculator
Given a known point (x1,y1) and slope m, find y at any target x using y=y1+m(x-x1). Useful for extending a line or reading off any y-value quickly.
How to use this tool
- Enter known x1, known y1, slope (m) and target x in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your y at target x and the full breakdown beneath it.
Formula
y = y1 + m(x - x1)
How it works
Substitute the known point and slope into y = y1 + m(x − x1) and evaluate at the target x.
Worked example
Point (2,3), slope 4, x=5
- y = 3 + 4(5-2)
- y = 3 + 12 = 15
Common mistakes to avoid
- Subtracting the target x from x1 instead of x1 from the target x, reversing the sign of the displacement.
- Adding m(x-x1) to zero instead of to y1, omitting the known point's y-value from the result.
- Confusing slope m with the run alone; slope is rise over run, a ratio, not just a horizontal distance.
Key terms
Frequently asked questions
- When should I use point-slope form instead of slope-intercept form?
- Point-slope is more convenient when you know a point on the line but have not yet computed the y-intercept. It avoids an extra rearrangement step.
- Can I find y for multiple x values without re-entering the known point each time?
- Yes. Once you know m and (x1,y1), substitute each new x value directly into y = y1 + m(x - x1).
- What does a slope of zero mean for the output?
- A slope of zero means the line is horizontal; y will equal y1 for every value of x.