https://file.aiquickdraw.com/mathbot/file/1726602464061znwmdyfr.jpg

To solve this question, we need to find the angle that the line with equation \( y = -x + 4 \) makes with the positive direction of the x-axis.

### Step-by-Step Explanation:

1. **Line Equation Form**:
   The equation of the line is \( y = -x + 4 \), which can be written in the slope-intercept form:
   \[
   y = mx + b
   \]
   where \( m \) is the slope of the line, and \( b \) is the y-intercept.

   In this case, \( m = -1 \) and \( b = 4 \).

2. **Relationship Between Slope and Angle**:
   The slope \( m \) of the line is related to the angle \( \theta \) it makes with the positive x-axis by the formula:
   \[
   m = \tan(\theta)
   \]
   So, we have:
   \[
   \tan(\theta) = -1
   \]

3. **Find the Angle**:
   To find \( \theta \), we use the inverse tangent (arctan) function:
   \[
   \theta = \tan^{-1}(-1)
   \]
   This gives us an angle of \( \theta = -45^\circ \). However, this is a negative angle, measured clockwise from the positive x-axis. To find the corresponding positive angle (measured counterclockwise), we add \( 180^\circ \):
   \[
   \theta = 180^\circ - 45^\circ = 135^\circ
   \]

Therefore, the angle that the line makes with the positive x-axis is **135°**.

### Correct Answer: C (135°)

---

Would you like further details or explanations on any step? Here are some related questions to deepen your understanding:

1. How does the slope of a line affect the angle it makes with the x-axis?
2. What is the significance of the negative sign in the slope of a line?
3. How can you find the angle for a line with a positive slope?
4. What is the general procedure to convert a negative angle to a positive angle?
5. How would the answer change if the slope was different, say \( m = -2 \)?

**Tip:** Remember, if a line's slope is negative, the angle it makes with the x-axis will always be greater than \( 90^\circ \) but less than \( 180^\circ \).

A straight line has the equation y = -x + 4. What angle does the line make with the positive direction of the x-axis?

This problem involves finding the angle a line makes with the x-axis. The equation of the line is y = -x + 4. Learn how to solve this using trigonometric relationships between slope and angle. The solution involves the arctangent function and adjusting for negative slopes. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation