https://file.aiquickdraw.com/mathbot/file/1730395413402py8uhuse.jpg

To find the equation of the line graphed in the image, we need to determine two key components: the slope and the y-intercept. The equation of a line in slope-intercept form is:

\[
y = mx + b
\]

where:
- \( m \) is the slope,
- \( b \) is the y-intercept.

### Step 1: Find the Slope (m)
The slope of a line is calculated as the change in \( y \) divided by the change in \( x \) between two points on the line:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

From the image, two points on the line are:
- \( (0, 7) \)
- \( (4, 4) \)

Using these points:
\[
m = \frac{4 - 7}{4 - 0} = \frac{-3}{4} = -\frac{3}{4}
\]

### Step 2: Identify the y-Intercept (b)
The y-intercept is where the line crosses the y-axis. From the point \( (0, 7) \), we can see that the line crosses the y-axis at \( y = 7 \). Therefore, \( b = 7 \).

### Step 3: Write the Equation
Now that we know the slope \( m = -\frac{3}{4} \) and the y-intercept \( b = 7 \), we can write the equation of the line:

\[
y = -\frac{3}{4}x + 7
\]

### Final Answer
The equation of the graphed line is:
\[
y = -\frac{3}{4}x + 7
\]

Would you like a breakdown of how to apply this to other problems, or have any other questions?

### Related Questions
1. How do you find the equation of a line if only given two points?
2. What are different forms of a linear equation (e.g., point-slope, standard form)?
3. How would you graph a line given its equation?
4. How can you find the x-intercept of a line from its equation?
5. What are parallel and perpendicular slopes?

### Tip
To check your answer, substitute one of the points into your equation to ensure it satisfies the line equation.

Learn how to find the equation of a line from a graph by identifying the slope and y-intercept. This example uses the points (0,7) and (4,4) to calculate the equation in slope-intercept form. Perfect for students in Grades 7-9 studying linear equations.

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