Question

a student was measuring the height of plants grown with different types of fertilizer or with plain water. he took his measurements using inches, then realized that he needed to use metric units, so he converted his measurements from inches to centimeters. using the graph below, determine the approximate height of plant a in centimeters.

plant	measurement in inches	measurement in centimeters
b	5	?
c	7.2	?
d	2	?

relationship between inches and centimeters
(graph: y - axis labeled “centimeters” with values 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30; x - axis labeled “inches” with values 0, 3, 6, 9, 12; a line passes through (0, 0) and a point (e.g., near (10, 25.4)) to show the inch - centimeter relationship)

Explanation:

Step1: Determine the conversion factor

From the graph, when inches = 10 (approximate x - value of the point), centimeters ≈ 25.4 (but we can also use the slope. The line passes through (0,0) and let's say the point is (10,25.4) approximately, but more accurately, we know that 1 inch = 2.54 cm. But from the graph, we can see the relationship is linear. Let's take two points: (0,0) and (10,25.4) (approximate). The slope (conversion factor) is $\frac{25.4}{10}=2.54$ cm per inch.

Step2: Convert plant A's height

Plant A has a height of 12 inches. To convert to centimeters, we use the formula: centimeters = inches×2.54. So, $12\times2.54 = 30.48\approx30$ (but looking at the graph, when x = 12, y (centimeters) is approximately 30 (since the line at x = 12 would be around 30 as the slope is 2.54, 12×2.54 = 30.48, which is approximately 30 or 31, but from the graph's scale, the point at x = 10 is around 25 - 27, so 12 inches would be around 30 (since 1 inch = 2.54 cm, 12×2.54 = 30.48, so approximately 30 or 31. But let's check the graph: the y - axis at x = 12, the line goes up to around 30 (since at x = 10, it's around 25 - 27, so x = 12 would be 12×2.54 = 30.48, so approximately 30 cm (or more accurately, 30.48, but the graph's point at x = 10 is around 25 - 27, so maybe the scale is such that 1 inch = 2.5 cm (approximate for simplicity). Then 12×2.5 = 30. So the approximate height is 30 cm (or 30.48 which is approximately 30 - 31). But from the graph, the line at x = 12 would be around 30 (since the y - axis at 30, and x = 12 is on the x - axis, the line connects (0,0) to (10,25 - 27) and beyond, so 12 inches would be approximately 30 cm (using 1 inch = 2.54 cm, 12×2.54 = 30.48, so approximately 30 or 31, but the most approximate from the graph is 30 (or 30.48 which is about 30).

Answer:

30.48 (or approximately 30 - 31, but more accurately 30.48, so the answer is approximately 30 cm (or 30.48 cm))