https://file.aiquickdraw.com/mathbot/file/1726443099007e0whpt4n.jpg

To find the equation of the line shown in the image, we need to follow these steps:

### Step 1: Identify the coordinates of two points on the line.
From the image, the two points appear to be:
- Point 1: \((-6, -2)\)
- Point 2: \((2, 2)\)

### Step 2: Calculate the slope of the line.
The slope \(m\) of the line is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the coordinates of the two points:
\[
m = \frac{2 - (-2)}{2 - (-6)} = \frac{2 + 2}{2 + 6} = \frac{4}{8} = \frac{1}{2}
\]
So, the slope of the line is \( \frac{1}{2} \).

### Step 3: Use the point-slope form of the equation of a line.
The point-slope form is given by:
\[
y - y_1 = m(x - x_1)
\]
We can use one of the points, say \((-6, -2)\), and the slope \( \frac{1}{2} \):
\[
y - (-2) = \frac{1}{2}(x - (-6))
\]
Simplifying:
\[
y + 2 = \frac{1}{2}(x + 6)
\]
Distribute the slope:
\[
y + 2 = \frac{1}{2}x + 3
\]
Subtract 2 from both sides to solve for \(y\):
\[
y = \frac{1}{2}x + 1
\]

### Final Answer:
The equation of the line is:
\[
y = \frac{1}{2}x + 1
\]

Would you like more details or have any questions about the steps?

---

Here are 5 related questions to further your understanding:
1. How do you find the slope if the coordinates are given in fraction form?
2. What is the general formula for the slope of a line?
3. Can you derive the equation using a different point on the line?
4. How does changing the slope affect the line's steepness?
5. What is the y-intercept of this line, and how do you interpret it?

**Tip:** Remember that the slope of a line indicates its steepness and direction. A positive slope means the line rises as it moves from left to right, while a negative slope means it falls.

Find an equation for the line passing through the points (-6, -2) and (2, 2) as shown in the graph.

Learn how to find the equation of a line passing through two points (-6, -2) and (2, 2). This problem involves key algebra concepts like slope calculation and the point-slope form of a linear equation. Suitable 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