https://file.aiquickdraw.com/mathbot/file/1726983036697l1gtfnmk.jpg

The graph in the image shows a straight line, and we are asked to write the equation of the line where \( y \) depends on \( x \). 

To write the equation of a straight line, we use the slope-intercept form:

\[
y = mx + b
\]

Where:
- \( m \) is the slope of the line, and
- \( b \) is the y-intercept (the point where the line crosses the y-axis).

### Step 1: Identify the y-intercept (\( b \))
From the graph, the line crosses the y-axis at \( y = 7 \), so:

\[
b = 7
\]

### Step 2: Calculate the slope (\( m \))
The slope \( m \) is the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. 

From the graph, two clear points are:
- \( (0, 7) \) (the y-intercept)
- \( (2, 4) \)

The slope \( m \) is calculated as follows:

\[
m = \frac{\text{rise}}{\text{run}} = \frac{4 - 7}{2 - 0} = \frac{-3}{2}
\]

### Step 3: Write the equation
Now that we know the slope \( m = -\frac{3}{2} \) and the y-intercept \( b = 7 \), the equation of the line is:

\[
y = -\frac{3}{2}x + 7
\]

Would you like further clarification, or do you have any questions?

Here are five related questions for practice:
1. What is the equation of a line with slope \( \frac{1}{2} \) and y-intercept \( 3 \)?
2. If the line passes through points \( (1, 4) \) and \( (-1, 2) \), how do you find its equation?
3. How do you determine the slope of a line given its equation in standard form \( Ax + By = C \)?
4. What is the slope of a line parallel to \( y = -\frac{3}{2}x + 7 \)?
5. How would the equation change if the line were shifted 3 units down?

**Tip:** When finding the slope, always carefully pick points where the line crosses grid intersections for more accurate calculations.

Write an equation for the graph, where y depends on x.

Learn how to find the equation of a line in slope-intercept form using the graph of a straight line. The problem focuses on identifying the slope and y-intercept from the graph. Suitable for students in Grades 8-10.

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