What Is The $x$-intercept Of The Function Below?$f(x) = \frac{7}{2} X - 2$A. \[$-2\$\]B. \[$\frac{4}{7}\$\]C. \[$-\frac{4}{7}\$\]D. \[$2\$\]

What is the $x$-intercept of the function below?

The $x$-intercept of a function is the point at which the graph of the function crosses the $x$-axis. In other words, it is the value of $x$ at which the function equals zero. To find the $x$-intercept of a linear function, we can set the function equal to zero and solve for $x$.

Finding the $x$-intercept of a Linear Function

A linear function is a function that can be written in the form $f(x) = mx + b$, where $m$ is the slope of the line and $b$ is the $y$-intercept. To find the $x$-intercept of a linear function, we can set the function equal to zero and solve for $x$.

Step 1: Set the function equal to zero

We start by setting the function equal to zero: $\frac{7}{2} x - 2 = 0$.

Step 2: Add 2 to both sides

Next, we add 2 to both sides of the equation to isolate the term with $x$: $\frac{7}{2} x = 2$.

Step 3: Multiply both sides by $\frac{2}{7}$

Now, we multiply both sides of the equation by $\frac{2}{7}$ to solve for $x$: $x = \frac{2}{\frac{7}{2}}$.

Step 4: Simplify the expression

To simplify the expression, we can multiply the numerator and denominator by 2: $x = \frac{2 \cdot 2}{\frac{7}{2} \cdot 2}$.

Step 5: Simplify the fraction

Now, we can simplify the fraction: $x = \frac{4}{7}$.

Conclusion

Therefore, the $x$-intercept of the function $f(x) = \frac{7}{2} x - 2$ is $\boxed{\frac{4}{7}}$.

Answer

The correct answer is B. $\boxed{\frac{4}{7}}$.

Discussion

This problem requires the student to find the $x$-intercept of a linear function. The student must first set the function equal to zero, then add 2 to both sides to isolate the term with $x$. Next, the student must multiply both sides by $\frac{2}{7}$ to solve for $x$. Finally, the student must simplify the expression to find the value of $x$. This problem requires the student to apply the concept of linear functions and to solve a linear equation.

Related Topics

• Finding the $y$-intercept of a linear function
• Graphing a linear function
• Solving a linear equation
• Finding the slope of a linear function

Practice Problems

• Find the $x$-intercept of the function $f(x) = 3x - 5$.
• Find the $y$-intercept of the function $f(x) = 2x + 1$.
• Graph the function $f(x) = x - 2$.
• Solve the equation $2x + 3 = 5$.
• Find the slope of the line $y = 2x + 1$.

Conclusion

In this article, we have discussed how to find the $x$-intercept of a linear function. We have shown that the $x$-intercept is the point at which the graph of the function crosses the $x$-axis. We have also provided a step-by-step guide on how to find the $x$-intercept of a linear function. Finally, we have provided some practice problems for the student to practice finding the $x$-intercept of a linear function.
Q&A: Finding the $x$-intercept of a Linear Function

Q: What is the $x$-intercept of a linear function?

A: The $x$-intercept of a linear function is the point at which the graph of the function crosses the $x$-axis. In other words, it is the value of $x$ at which the function equals zero.

Q: How do I find the $x$-intercept of a linear function?

A: To find the $x$-intercept of a linear function, you can set the function equal to zero and solve for $x$. This involves adding or subtracting a constant to both sides of the equation, then multiplying or dividing both sides by a coefficient to isolate the term with $x$.

Q: What is the first step in finding the $x$-intercept of a linear function?

A: The first step in finding the $x$-intercept of a linear function is to set the function equal to zero. This means that you will replace the $y$-value in the function with zero.

Q: How do I add or subtract a constant to both sides of the equation?

A: To add or subtract a constant to both sides of the equation, you can simply add or subtract the constant from both sides. For example, if you have the equation $2x + 3 = 5$, you can subtract 3 from both sides to get $2x = 2$.

Q: How do I multiply or divide both sides of the equation by a coefficient?

A: To multiply or divide both sides of the equation by a coefficient, you can simply multiply or divide both sides by the coefficient. For example, if you have the equation $2x = 2$, you can divide both sides by 2 to get $x = 1$.

Q: What is the final step in finding the $x$-intercept of a linear function?

A: The final step in finding the $x$-intercept of a linear function is to simplify the expression to find the value of $x$. This may involve multiplying or dividing fractions, or simplifying complex expressions.

Q: Can I use a calculator to find the $x$-intercept of a linear function?

A: Yes, you can use a calculator to find the $x$-intercept of a linear function. However, it is often more efficient to solve the equation by hand, especially for simple linear functions.

Q: What are some common mistakes to avoid when finding the $x$-intercept of a linear function?

A: Some common mistakes to avoid when finding the $x$-intercept of a linear function include:

• Forgetting to set the function equal to zero
• Not isolating the term with $x$
• Not simplifying the expression to find the value of $x$
• Using a calculator incorrectly

Q: How can I practice finding the $x$-intercept of a linear function?

A: You can practice finding the $x$-intercept of a linear function by working through example problems, such as those provided in this article. You can also try creating your own example problems and solving them on your own.

Q: What are some real-world applications of finding the $x$-intercept of a linear function?

A: Finding the $x$-intercept of a linear function has many real-world applications, including:

• Modeling population growth
• Predicting stock prices
• Calculating the cost of goods
• Determining the slope of a line

Conclusion

In this article, we have provided a Q&A guide to finding the $x$-intercept of a linear function. We have covered the basics of finding the $x$-intercept, including setting the function equal to zero, isolating the term with $x$, and simplifying the expression to find the value of $x$. We have also provided some common mistakes to avoid and some real-world applications of finding the $x$-intercept of a linear function.