https://file.aiquickdraw.com/mathbot/file/17266899845191eof4ana.jpg

Which equation best represents the slope-intercept form of the line that passes through point P and is parallel to line m?
A.y=32x − 5

B.y=−23x + 23

C.y=32x + 5

D.y=−23x −23


To determine which equation best represents the slope-intercept form of the line that passes through point \( P \) and is parallel to line \( m \), we follow these steps:

### 1. Identify the slope of the given line \( m \)
The equation of a line in slope-intercept form is:

\[
y = mx + b
\]

Where:
- \( m \) is the slope
- \( b \) is the y-intercept

By examining the image, the line \( m \) moves from the bottom left to the top right, indicating a positive slope. The line crosses grid points, so we can calculate the slope by using two points on the line.

Let’s take two points that the line \( m \) passes through:
- At \( (0, -3) \)
- At \( (3, 3) \)

The slope \( m \) is calculated as:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - (-3)}{3 - 0} = \frac{6}{3} = 2
\]

Thus, the slope of the line \( m \) is \( 2 \).

### 2. Equation of the line parallel to \( m \)
Lines that are parallel have the same slope. Therefore, the slope of the line passing through point \( P \) will also be \( 2 \).

### 3. Determine the coordinates of point \( P \)
From the graph, point \( P \) is located at approximately \( (-2, 2) \).

### 4. Use the point-slope form to find the equation of the line
The point-slope form of a line is:

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

Where:
- \( m \) is the slope (which is 2)
- \( (x_1, y_1) \) are the coordinates of point \( P \) (which is \( (-2, 2) \))

Substitute the values:

\[
y - 2 = 2(x - (-2)) \quad \Rightarrow \quad y - 2 = 2(x + 2)
\]

Simplify:

\[
y - 2 = 2x + 4 \quad \Rightarrow \quad y = 2x + 6
\]

### 5. Conclusion
The equation of the line that passes through point \( P \) and is parallel to line \( m \) is:

\[
y = 2x + 6
\]

Since this does not directly match any of the options, I suspect the image's slope might involve an inversion I didn't account for. However, I can guide through the next steps.

Would you like to explore related questions or clarifications?

Which equation best represents the slope-intercept form of the line that passes through point P and is parallel to line m?
A.y=32x − 5
B.y=−23x + 23
C.y=32x + 5
D.y=−23x −23

Explore how to find the slope-intercept form of a line parallel to another, passing through a specific point. This example walks through calculating the slope from two points, applying the point-slope formula, and converting to slope-intercept form. Suitable for Grades 9-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation