Calculate the size of the angle between the line y = 4x+3 and the x-axis.

The equation of the line is \( y = 4x + 3 \). The slope of the line is given by the coefficient of \( x \), which is 4.

To find the angle \( \theta \) between the line and the x-axis, we use the formula:

\[
\tan(\theta) = \text{slope of the line}
\]

In this case, the slope is 4, so:

\[
\tan(\theta) = 4
\]

Now, to find \( \theta \), we take the arctangent (inverse tangent) of 4:

\[
\theta = \tan^{-1}(4)
\]

Let me calculate this value for you.

The angle between the line \( y = 4x + 3 \) and the x-axis is approximately \( 75.96^\circ \).

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the angle change if the slope of the line was negative?
2. What is the angle between the line \( y = -4x + 3 \) and the x-axis?
3. How can you find the angle between two intersecting lines?
4. What is the relationship between the slope and angle in general?
5. How does the y-intercept affect the orientation of the line?

**Tip:** When a line has a positive slope, the angle between the line and the x-axis is always less than \( 90^\circ \), but greater than \( 0^\circ \).

Calculate the size of the angle between the line y = 4x + 3 and the x-axis.

This page provides a detailed solution to the problem of calculating the angle between the line y = 4x + 3 and the x-axis. Using key algebraic and trigonometric concepts like slopes and the arctangent function, the solution is suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation