Math Problem Statement

This scatterplot shows the number of blocks and the height of 20 different block towers. The highlighted point represents a block tower that has 18 blocks. What is the height of this block tower? x y 4 6 8 10 12 14 16 18 20 22 24 10 20 30 40 50 60 70 80 90 Number of blocks Tower height (inches) The height of this block tower is 50 inches. Excellent! The line y = 3x is a model of the relationship between the number of blocks and the height of a block tower. This model has been graphed on the scatterplot. If a block tower has 18 blocks, what does the model predict for the height? You can substitute 18 into the equation that represents the linear model. Start by substituting 18 blocks for x. x y (18, 50) 4 6 8 10 12 14 16 18 20 22 24 10 20 30 40 50 60 70 80 90 Number of blocks Tower height (inches) y = 3x

y = 3· Excellent! Now, solve for the value of y to determine what the model predicts. (18, 50) 4 6 8 10 12 14 16 18 20 22 24 10 20 30 40 50 60 70 80 90 Number of blocks Tower height (inches) y = 3x

y = 3·18

y =

Solution

To find the height predicted by the model y=3xy = 3x when there are 18 blocks, we substitute x=18x = 18 into the equation.

y=3×18=54y = 3 \times 18 = 54

So, the model predicts that the height of a block tower with 18 blocks is 54 inches.

Let me know if you'd like further explanation or have more questions!

Here are some follow-up questions you might find interesting:

  1. How would the height change if the number of blocks increased to 20?
  2. What does the slope of the equation y=3xy = 3x represent in the context of this problem?
  3. How does the model compare to the actual data point for 18 blocks, which had a height of 50 inches?
  4. What happens to the height if there were only 5 blocks in the tower?
  5. If the model were changed to y=4xy = 4x, how would this affect the height of a tower with 18 blocks?

Tip: In a linear model y=mx+by = mx + b, the slope mm tells you how much the dependent variable (y) changes for each unit increase in the independent variable (x).

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Math Problem Analysis

Mathematical Concepts

Linear Relationships
Algebra
Linear Models

Formulas

y = 3x

Theorems

Linear model prediction

Suitable Grade Level

Grades 7-9

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