How to find the zero of a linear function?
Understand the Problem
The question is asking how to determine the value of the input (usually x) at which a linear function equals zero. This involves setting the function's equation to zero and solving for the variable.
Answer
The value of \( x \) is given by \( x = -\frac{b}{m} \).
Answer for screen readers
The value of the input ( x ) where the linear function equals zero is given by the equation: $$ x = -\frac{b}{m} $$
Steps to Solve
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Identify the Linear Function First, you need to clearly define the linear function you are working with. For example, let’s say the function is given as $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
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Set the Function Equal to Zero Next, to find where the function equals zero, set the equation equal to zero: $$ f(x) = 0 $$
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Substitute the Function Into the Equation Substituting in our function yields: $$ mx + b = 0 $$
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Isolate the Variable Now, solve for $x$ by isolating it. First, subtract $b$ from both sides: $$ mx = -b $$
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Solve for $x$ Finally, divide both sides by $m$ to find the value of $x$: $$ x = -\frac{b}{m} $$
The value of the input ( x ) where the linear function equals zero is given by the equation: $$ x = -\frac{b}{m} $$
More Information
This result shows the x-intercept of the linear function, which is the point where the graph crosses the x-axis. It's an important concept in understanding linear equations and their graphs.
Tips
- Forgetting to set the function equal to zero. Always remember that you need to find where the function touches the x-axis.
- Failing to isolate the variable correctly can lead to incorrect results. Take your time to move all constants to one side before dividing by the coefficient of $x$.
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