Linear function value

Type slope a, intercept b and the argument x. The linear function value is y = ax + b. 2, 3 and 4 give 11. 1, 0 and 5 give 5. 0, 7 and 10 give 7.

Field order is a, b, x. The calculator computes a*c + b, where c is x. This is not interpolation between two points.

Input data

Results

Enter data and click Calculate.

How it works

The value of a linear function y = ax + b at x is the slope times x plus the intercept. With a = 2, b = 3 and x = 4 you have 2 × 4 + 3 = 11. The calculator multiplies the first field by the third and adds the second.

The fields are a, b and x. 1, 0 and 5 give 5, because y = 1·5 + 0. A line through the origin. 0, 7 and 10 give 7: slope zero, y stays at the intercept no matter what x is.

A minus in a drops the line. a = −2, b = 3, x = 4 give −5. A minus in b shifts the graph down.

Linear interpolation is on the neighbouring page and finds y between two points (x₁, y₁) and (x₂, y₂). Here you know the formula, not a segment.

The header units switch does not multiply anything. 2, 3 and 4 stay 11 whatever the label says.

2, 3 and 4 give 11. 1, 0 and 5 give 5. 0, 7 and 10 give 7. That is the whole card: y = ax + b.

Formula

y = a · x + b

How to use

  1. Type a, b and x, for example 2, 3 and 4.
  2. Click Calculate. y comes out 11.
  3. 1, 0 and 5 give 5. 0, 7 and 10 give 7.
  4. The first field is the slope, the second the intercept, the third x.
  5. A point between two nodes lives on linear interpolation.

2, 3 and 4 give 11

y = ax + b. 2, 3 and 4 give 11. 1, 0 and 5 give 5. 0, 7 and 10 give 7.

function
y at one x. 2, 3 and 4 give 11. This is not a list of points.
linear
The line y = ax + b. Slope a, intercept b. 0, 7 and 10 give 7.
intercept
Field b. When a = 0, only b remains. 1, 0 and 5 give 5, because the intercept is zero.

Examples

Example 1

  • a = 2
  • b = 3
  • x = 4

11

What is y with a = 2, b = 3, x = 4? 11. 2 × 4 + 3.

Example 2

  • a = 1
  • b = 0
  • x = 5

5

What is y with a = 1, b = 0, x = 5? 5. A line through zero.

Example 3

  • a = 0
  • b = 7
  • x = 10

7

What is y with a = 0, b = 7, x = 10? 7. Horizontal, y = b.

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Common questions

What is y with a = 2, b = 3 and x = 4?

11. 2 × 4 + 3. The calculator computes a*x + b.

What does linear function value mean?

y = ax + b at one x. Slope, intercept, argument.

What do 1, 0 and 5 give?

5. y = x, because b = 0.

What do 0, 7 and 10 give?

7. Slope zero, y stays at 7 for every x.

Which field is x?

The third. The first is a, the second b. Easy to mix up with interpolation.

Does a negative a pass?

Yes. −2, 3 and 4 give −5.

How is this different from interpolation?

Here you know a and b. There, two points and an x between them. Other fields.

Does an x outside some range lock the calculator?

No. The algebra ax + b does not ask for a segment.

Where is a line from two points?

On linear interpolation. Here you type slope and intercept.

Does a comma in 2.5 work?

Yes. 2.5, 3 and 4 give 13.

Knowledge sources

The calculator computes the same formula as the definition below.

Page updated in 2026.