Question

5
actual distance (mi)
map distance (in.)
0 2 4 6
0
30
60
90

Explanation:

Since the problem isn't fully stated (e.g., what to find: slope, equation, actual distance for a map distance, etc.), let's assume we need to find the scale (ratio of actual distance to map distance) or the equation of the line.

Looking at the points: (2, 15)? Wait, no, the y-axis is Actual Distance (mi), x-axis Map Distance (in). Let's check the points. At x=2, y=15? Wait, the grid: from 0 to 30, 60, 90. Let's see the first point at x=2, y=15? Wait, no, maybe the points are (2, 15), (4, 30), (6, 45)? Wait, no, the blue dots: at x=2, y=15? Wait, maybe the scale is 1 in = 7.5 mi? Wait, no, let's calculate the slope (rate of change).

Suppose we take two points: (2, 15) and (4, 30). Wait, no, maybe the y-axis is labeled with 0, 30, 60, 90. So the first dot at x=2, y=15? No, maybe the grid lines: between 0 and 30, there's one line, so each grid square is 15 mi? Wait, no, let's re-express.

Wait, the x-axis: 0, 2, 4, 6 (map distance in inches). The y-axis: 0, 30, 60, 90 (actual distance in miles). Let's take the points:

• When x=2 (in), y=15 (mi)? No, the first blue dot is at x=2, y=15? Wait, no, maybe the points are (2, 15), (4, 30), (6, 45)? No, the second dot at x=4, y=30, third at x=6, y=45? Wait, no, the third dot is between 30 and 60, maybe 45? Wait, no, the y-axis has 30, 60, 90. So from 0 to 30 is one interval, 30 to 60 another, 60 to 90 another. So the first dot at x=2, y=15? No, maybe the scale is 1 inch = 7.5 miles? Wait, no, let's do it properly.

Let's assume we need to find the constant of proportionality (k) where y = kx (since it's a proportional relationship, passes through origin).

Take the point (4, 30): y = 30 when x=4. So k = y/x = 30/4 = 7.5. Wait, 30 divided by 4 is 7.5. Then for x=2, y=27.5=15, which matches the first dot (x=2, y=15). For x=6, y=67.5=45? But the third dot is at x=6, y=45? Wait, but the y-axis at 60 is above, so maybe my initial assumption is wrong.

Wait, maybe the y-axis is labeled with 0, 30, 60, 90, so each major grid line is 30 miles. So between 0 and 30, there are two grid lines (so three intervals), meaning each interval is 10 miles? No, this is confusing. Alternatively, maybe the points are (2, 30), (4, 60), (6, 90)? No, the first dot is at x=2, y=30? No, the first dot is below 30. Wait, maybe the y-axis is misread. Let's start over.

The graph shows a proportional relationship (straight line through origin) between map distance (x, in) and actual distance (y, mi). Let's pick two points:

• Point 1: (2, 15) – no, maybe (2, 30)? No, the first dot is at x=2, y=15? Wait, the user's graph: x-axis (map distance) has 0, 2, 4, 6. y-axis (actual distance) has 0, 30, 60, 90. The blue dots:

• First dot: x=2, y=15 (midway between 0 and 30)

• Second dot: x=4, y=30 (at 30)

• Third dot: x=6, y=45 (midway between 30 and 60)

Wait, that makes sense. So the relationship is y = 7.5x, since when x=2, y=15 (27.5=15), x=4, y=30 (47.5=30), x=6, y=45 (6*7.5=45). So the constant of proportionality (scale) is 7.5 miles per inch.

If the question is "What is the scale of the map (miles per inch)?" or "Find the equation of the line relating map distance to actual distance," here's the solution:

Step1: Identify two points

Take (x1, y1) = (2, 15) and (x2, y2) = (4, 30) (or (6, 45)).

Step2: Calculate the slope (k)

Slope \( k = \frac{y2 - y1}{x2 - x1} = \frac{30 - 15}{4 - 2} = \frac{15}{2} = 7.5 \).

Step3: Equation of the line

Since it's proportional (passes through origin), \( y = kx = 7.5x \), where x is map distance (in), y is actual distance (mi).

Answer:

The scale is 7.5 miles per inch, or the equation is \( y = 7.5x \).

But since the problem isn't fully stated, this is a common interpretation (finding the scale or equation from the graph of map distance vs. actual distance, which is a proportional relationship).