https://file.aiquickdraw.com/mathbot/file/1728582034818ijp0groq.jpg

The image shows a graph of a straight line. To find the equation of the line, we need to identify its slope and y-intercept. Let's analyze this step by step:

### 1. Identifying Points
We can see two clear points on the line:
- The point \((-6, 4)\)
- The point \((0, -1)\), which is the y-intercept.

### 2. Slope Calculation
The formula for the slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \((-6, 4)\) and \((0, -1)\):
\[
m = \frac{-1 - 4}{0 - (-6)} = \frac{-5}{6}
\]

### 3. Equation of the Line
The slope-intercept form of a line is:
\[
y = mx + b
\]
where \(m\) is the slope and \(b\) is the y-intercept. From the graph, the y-intercept is \(b = -1\).

Thus, the equation of the line is:
\[
y = -\frac{5}{6}x - 1
\]

Would you like more details or have any questions?

Here are some related questions to expand your understanding:
1. How do you find the equation of a line if you only have one point and the slope?
2. What is the relationship between the slope and the steepness of the line?
3. How can you rewrite the equation in standard form \(Ax + By = C\)?
4. What happens to the graph if the slope becomes positive?
5. How can you find the x-intercept from the equation of the line?

**Tip**: Remember, the slope tells you how much \(y\) changes for each unit of change in \(x\), which helps you visualize the steepness and direction of the line.

Find an equation for the line shown in the graph.

Learn how to find the equation of a line given a graph. The solution covers how to calculate the slope and y-intercept, using points like (-6, 4) and (0, -1). Suitable for students in Grades 8-10.

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