https://file.aiquickdraw.com/mathbot/file/1727462379251m4oclqhb.jpg

Let's break down the problem from the image step by step.

We are given:
1. The slope of the line, \( m = \frac{2}{7} \).
2. A point on the line, \( (-9, 6) \).
3. We need to find the \( y \)-coordinate of another point, \( (5, y) \).

We can use the **point-slope form of the equation of a line**:

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

Where:
- \( m = \frac{2}{7} \) (the slope),
- \( (x_1, y_1) = (-9, 6) \) (the given point),
- \( (x, y) = (5, y) \) (the point we're trying to find the \( y \)-coordinate for).

Substitute these values into the equation:

\[
y - 6 = \frac{2}{7}(x - (-9))
\]
\[
y - 6 = \frac{2}{7}(x + 9)
\]

Now, substitute \( x = 5 \) into this equation:

\[
y - 6 = \frac{2}{7}(5 + 9)
\]
\[
y - 6 = \frac{2}{7}(14)
\]
\[
y - 6 = 2 \times 2
\]
\[
y - 6 = 4
\]
\[
y = 4 + 6 = 10
\]

Therefore, the missing \( y \)-coordinate is \( 10 \). The point is \( (5, 10) \).

Would you like more details on this process, or do you have any questions? Here are some related questions:

1. How do you convert the slope-intercept form to point-slope form?
2. What does the slope of a line represent in real-world situations?
3. Can you find the equation of the line passing through the points \( (-9, 6) \) and \( (5, 10) \)?
4. How do you find the midpoint between two points on a line?
5. What happens to the slope of a line when the coordinates of the points change direction?

**Tip**: Always substitute carefully in slope-related problems to avoid errors with signs!

The slope of the line is 2/7, and you know it goes through the point (-9, 6). Another point on the line goes through the x-coordinate 5. Find the missing y-coordinate (5, ___).

Learn how to find the missing y-coordinate of a line with a given slope (2/7) and a point (-9, 6). This step-by-step solution uses the point-slope form of the line equation, perfect 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