Let's analyze the problem from the image you provided.

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.