https://file.aiquickdraw.com/mathbot/file/1727110258166fic9wdku.jpg

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The point given is \((d, 4)\), which means the y-coordinate is \(4\). We need to find the value of \(d\) for which this point lies on the line shown in the graph.

Steps to solve:
1. Identify the equation of the line from the graph. The line has a negative slope, so we can determine the slope and y-intercept from two points on the line.
2. Once we have the equation, substitute \(y = 4\) into the equation to find the corresponding \(x\)-value, which is \(d\).

From the graph:
- One point on the line is \((0, 8)\) (y-intercept).
- Another point is \((4, 6)\).

We can calculate the slope \(m\) as:
\[
m = \frac{6 - 8}{4 - 0} = \frac{-2}{4} = -\frac{1}{2}
\]
Now we use the point-slope form of the line equation:
\[
y = mx + b
\]
Substitute the slope \(-\frac{1}{2}\) and the y-intercept \(8\):
\[
y = -\frac{1}{2}x + 8
\]
Next, substitute \(y = 4\) to find \(x = d\):
\[
4 = -\frac{1}{2}d + 8
\]
Solve for \(d\):
\[
4 - 8 = -\frac{1}{2}d
\]
\[
-4 = -\frac{1}{2}d
\]
\[
d = 8
\]

Thus, the value of \(d\) is \(8\).

Would you like more details or explanations on any part of this solution?

Here are five related questions to explore:
1. What is the slope of a line perpendicular to the one given in the problem?
2. How can you determine the equation of a line from any two points?
3. If the point \((d, 4)\) had different y-values, how would the method change to find \(d\)?
4. How do you find the slope of a line when only its graph is provided?
5. What is the difference between point-slope form and slope-intercept form of a line equation?

**Tip:** When finding the equation of a line from a graph, always look for two points with integer coordinates to easily calculate the slope.

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

Determine the value of d for the point (d, 4) lying on a line with a negative slope. This solution explores key linear equation concepts, including the slope formula and solving for unknown coordinates. Suitable for students in Grades 8-10.

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