Point Slope Line CalculatorFree online math calculator — instant results, no sign-up
Evaluate a line from a known point, slope and target x coordinate.
About the Point Slope Line Calculator
The Point Slope Line Calculator finds the y coordinate on a straight line at a target x coordinate using a known point and the line’s slope. It also calculates the y intercept, so you can express the same line in slope-intercept form. With slope 2, known point (1, 3), and target x 5, it returns target y 11 and y intercept 1.
- Slope
- The slope is the change in y per unit change in x, measured in y-units per x-unit, with a default of 2.
- Known x
- The known x is the horizontal coordinate of a point on the line, measured in the same x-units as Target x, with a default of 1.
- Known y
- The known y is the vertical coordinate paired with Known x, measured in y-units, with a default of 3.
- Target x
- The target x is the horizontal coordinate where you want to evaluate the line, measured in the same x-units as Known x, with a default of 5.
Formula and method
Point-slope form: y − y₁ = m(x − x₁). Target y: yₜ = y₁ + m(xₜ − x₁). Y intercept: b = y₁ − mx₁. With the defaults: yₜ = 3 + 2(5 − 1) = 11; b = 3 − 2(1) = 1. The resulting line is y = 2x + 1.
- mThe line’s slope, in y-units per x-unit.
- x₁The known point’s x coordinate.
- y₁The known point’s y coordinate.
- xₜThe target x coordinate.
- yₜThe calculated y coordinate at the target x.
- bThe y intercept, or the value of y where x = 0.
- x, yThe coordinates of any point on the line.
Subtract the known x from the target x to find the horizontal change, multiply that change by the slope, and add the result to the known y. Separately, subtract the product of the slope and known x from the known y to obtain the y intercept. For the default inputs, the horizontal change is 5 − 1 = 4, the vertical change is 2 × 4 = 8, and the target y is 3 + 8 = 11; the y intercept is 3 − 2 × 1 = 1.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Slope2
- Known x1
- Known y3
- Target x5
Results
- Target y11
- Y intercept1
How to use the Point Slope Line Calculator
- 1Enter the line’s slope in Slope; use 2 for the worked example.
- 2Enter the known point using Known x = 1 and Known y = 3.
- 3Enter Target x = 5 to evaluate the line at that horizontal coordinate.
- 4Read Target y = 11, which places the evaluated point at (5, 11).
- 5Read Y intercept = 1 and use it with the slope to write the line as y = 2x + 1.
Reading your result
The Target y row gives the line’s y coordinate at your chosen Target x, in the same units as Known y; the default result of 11 means (5, 11) lies on the line. The Y intercept row gives the line’s y coordinate where x = 0, also in y-units; the default result of 1 means the line crosses the y-axis at (0, 1). Changing Target x changes the evaluated point but does not change the line’s y intercept.
Limitations
The calculation assumes a straight line with a constant, finite slope and consistent coordinate units. Vertical lines cannot be represented by a finite slope and do not generally give a unique y value for a target x. Inputs may be unitless or represent physical quantities, but this calculation does not convert units. When the line models real data, predictions outside the observed range may not remain valid. Decimal calculations may be affected by numerical rounding.
Common questions
Why does the default Target y equal 11 rather than 10?+
Multiplying the slope by Target x alone ignores the line’s offset. The known point (1, 3) gives a y intercept of 1, so the target value is 2 × 5 + 1 = 11.
Does changing Target x change the Y intercept?+
No. The y intercept depends only on the slope and the known point: b = y₁ − mx₁. Target x only selects where to evaluate that fixed line.
What happens when Target x equals Known x?+
The horizontal change is zero, so Target y equals Known y. This follows directly from yₜ = y₁ + m(xₜ − x₁).
Can this calculator evaluate horizontal or vertical lines?+
A horizontal line is supported by entering a slope of zero; Target y and Y intercept then both equal Known y. A vertical line has an undefined slope and cannot be evaluated with this point-slope calculation.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
You might also like
Vector Addition Calculator
Add two two-dimensional vectors component by component.
Vector Magnitude Calculator
Calculate the magnitude of a three-dimensional vector.
Dot Product Calculator
Calculate the dot product of two three-dimensional vectors.
Cross Product Calculator
Calculate the cross product of two three-dimensional vectors.
Angle Between Vectors Calculator
Calculate the angle between two three-dimensional vectors.
Two Linear Equations Calculator
Solve two independent linear equations in two unknowns.
Results are estimates for informational purposes and are not financial, medical or legal advice.