show work: Find the​ slope-intercept form of the equation of the line that passes through the point P and makes angle thetaθ with the positive​ x-axis.
Pequals=​(44​,55​), thetaθequals=4545degrees°

To find the equation of the line in slope-intercept form, we can follow these steps:

### 1. Determine the slope of the line.
The slope \( m \) of a line that makes an angle \( \theta \) with the positive x-axis is given by:

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

Given \( \theta = 45^\circ \), we can compute the slope:

\[
m = \tan(45^\circ) = 1
\]

### 2. Use the point-slope form of the equation of a line.
The point-slope form of the equation of a line is:

\[
y - y_1 = m(x - x_1)
\]

where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope. The given point is \( P(44, 55) \), and the slope \( m = 1 \). Substituting these values into the point-slope form:

\[
y - 55 = 1(x - 44)
\]

### 3. Simplify to slope-intercept form.
Now, simplify the equation to the slope-intercept form \( y = mx + b \):

\[
y - 55 = x - 44
\]

Add 55 to both sides:

\[
y = x + 11
\]

### Final answer:
The slope-intercept form of the equation of the line is:

\[
y = x + 11
\]

Do you have any questions or want more details? 

Here are 5 related questions to expand your understanding:
1. How do you find the slope of a line given two points?
2. What is the significance of the slope-intercept form in geometry?
3. How does the angle \( \theta \) relate to the direction of the line?
4. Can you explain how to find the slope when the angle is not 45 degrees?
5. How do we find the x-intercept and y-intercept from the slope-intercept form?

**Tip:** For any angle \( \theta \), you can always compute the slope using \( \tan(\theta) \), making sure your angle is measured in degrees or radians correctly.

Find the slope-intercept form of the equation of the line that passes through the point P and makes angle θ with the positive x-axis. P = (44, 55), θ = 45°.

This guide explains how to find the slope-intercept form of a line that passes through the point P(44, 55) and makes an angle of 45° with the positive x-axis. Key concepts include using trigonometry to determine the slope and applying point-slope and slope-intercept forms of a line. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation