Linear function
Zero of a linear function
A zero is an x value for which the function has value 0. On the graph, it is the point where the line crosses the X-axis.
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How do you calculate the zero?
It is enough to assume that y = 0. For the formula y = ax + b you solve the equation:
Equation to solve
ax + b = 0
When a is not equal to 0, simply transform the equation and calculate x.
Set the function value to 0.
At the zero, the graph crosses the X-axis, so the value of y is 0.
Solve the equation for x.
Move the constant term to the other side and divide by the coefficient of x.
X-axis intercept
On the graph, we look for the place where the line crosses the horizontal X-axis. Then the function value is equal to 0.
f(x) = 2x - 2
Ready formula
Zero of a linear function
We use this formula when coefficient a is different from 0.
x = -ba
Example: f(x) = 2x - 2
Step 1
2x - 2 = 0
We substitute 0 for f(x), because we are looking for the zero.
Step 2
2x = 2
We move -2 to the other side of the equation.
Step 3
x = 1
We divide both sides by 2 and get the result.
After solving the equation, we get the x value for which the function equals 0.
The zero is x = 1, so the graph crosses the X-axis at (1, 0).
Watch out for constant functions
When a = 0, the function has the form y = b. If b = 0, every x is a zero. If b is different from 0, the function has no zero.
b = 0
Every x is a zero.
b ≠ 0
The function has no zero.