🏠 The starting value b

In the previous section, we discussed the slope (a). The second number we need for the formula y = ax + b is the starting value b.

The value of b indicates where the graph intersects the y-axis. This is the value of y when x = 0.

Interactive Graph:
Drag the points in the tool. You will see that as soon as the line shifts, the point on the y-axis (the starting value b) immediately changes with it.

🖋️ Setting up the equation

To create the equation of a line, you need two puzzle pieces:

The slope (a).
One point (x, y) that the line passes through.

Example:

Set up a formula for the line with slope = 2 that passes through point A(1, 4).

Start with the standard form: y = ax + b
Substitute the slope (a): y = 2x + b
Substitute the coordinates of point A (x = 1 and y = 4):
4 = 2 · 1 + b
Solve for b:
4 = 2 + b → b = 2
Write down the complete formula:
y = 2x + 2

📋 Step-by-step plan: To the formula in 5 steps

1. Write down the basic form: y = ax + b.
2. Calculate or find the value of a (the slope).
3. Choose a known point on the line and substitute the x and y.
4. Calculate the starting value b by solving the equation.
5. Write down the final formula with the found a and b.

💡

Did you know? The starting value b in engineering is often called the "offset" or the "zero setting" of a sensor or measuring instrument.