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To find the value of \( d \) for the point \( (d, 4) \) that lies on the line, we need to determine the equation of the line shown in the graph. Let's break this down:

### 1. Determine the slope (m) of the line:
We can pick two clear points from the graph to calculate the slope. The points \( (0, 6) \) and \( (8, 0) \) are on the line.

The slope \( m \) of a line is calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, 6) \) and \( (8, 0) \):
\[
m = \frac{0 - 6}{8 - 0} = \frac{-6}{8} = -\frac{3}{4}
\]

### 2. Write the equation of the line:
The general equation of a line is:
\[
y = mx + b
\]
We know the slope \( m = -\frac{3}{4} \), and we can substitute the point \( (0, 6) \) to find the y-intercept \( b \):
\[
6 = -\frac{3}{4}(0) + b \quad \Rightarrow \quad b = 6
\]
So, the equation of the line is:
\[
y = -\frac{3}{4}x + 6
\]

### 3. Substitute the known \( y \)-coordinate:
We know the point \( (d, 4) \) lies on the line, so substitute \( y = 4 \) into the equation:
\[
4 = -\frac{3}{4}d + 6
\]

### 4. Solve for \( d \):
Subtract 6 from both sides:
\[
4 - 6 = -\frac{3}{4}d
\]
\[
-2 = -\frac{3}{4}d
\]
Multiply both sides by \( -\frac{4}{3} \):
\[
d = -2 \times -\frac{4}{3} = \frac{8}{3}
\]

Thus, the value of \( d \) is \( \frac{8}{3} \).

However, none of the multiple-choice options exactly match this value, which suggests a need to recheck the calculations or the graph. Would you like a deeper breakdown or explanation of why this might not align with the provided options? Here are 5 related questions for expansion:

1. How do we determine the intercepts of a line from a graph?
2. What is the process for finding the slope if the points are unclear on the graph?
3. How do fractional values affect the graphing of lines?
4. What is the significance of verifying units and axes in graph problems?
5. Why might real-world contexts cause approximations in graph-based problems?

**Tip:** Always verify if the graph scale or units are uniform across axes when dealing with multiple-choice problems involving graphs!

The point with coordinates (d, 4) lies on the line shown. What is the value of d?

Solve the problem of determining the value of d for a point that lies on a line. This solution involves calculating the slope and writing the equation of a line, suitable for students in grades 9-10.

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