For what values of x does the function y=2x+13 have a positive value? a negative value?

The function given is \( y = 2x + 13 \).

### 1. Positive Value:
To find when the function \( y = 2x + 13 \) is positive, we set:

\[
2x + 13 > 0
\]

Solve for \( x \):

\[
2x > -13
\]
\[
x > -\frac{13}{2}
\]
\[
x > -6.5
\]

Thus, the function is positive when \( x > -6.5 \).

### 2. Negative Value:
To find when the function \( y = 2x + 13 \) is negative, we set:

\[
2x + 13 < 0
\]

Solve for \( x \):

\[
2x < -13
\]
\[
x < -6.5
\]

Thus, the function is negative when \( x < -6.5 \).

### Conclusion:
- **Positive value**: \( x > -6.5 \)
- **Negative value**: \( x < -6.5 \)

Would you like more details or have any questions?

---

Here are some related questions:
1. What is the value of \( y \) when \( x = 0 \)?
2. For what values of \( x \) does the function \( y = 2x + 13 \) equal zero?
3. How does the slope of the function \( y = 2x + 13 \) affect its graph?
4. What is the general form of a linear function like \( y = 2x + 13 \)?
5. What is the domain and range of the function \( y = 2x + 13 \)?

**Tip**: In linear functions, the slope determines how steep the line is, and the y-intercept shifts the line vertically.

Discover how to find the values of x where the linear function y = 2x + 13 is positive or negative. This solution covers key algebraic concepts such as solving linear inequalities and analyzing linear functions, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation