Problems 4-75 to 4-77 in Lesson 4.3.1 cover area/perimeter of algebra tile shapes, simplifying expressions, and analyzing graphs for proportionality.
4-75: This problem involves finding the area and perimeter of a shape made with algebra tiles.
Sketch the shape: Reproduce the arrangement of algebra tiles shown in the problem.
Find the area: Count and add the areas of each individual tile. For example, if you have 2 x-tiles and 1 y-tile, the area would be 2x + y.
Find the perimeter: Label the sides of the shape with their corresponding lengths (e.g., x, y, 2, etc.) and add all the side lengths together.
Rearrangement and area: The area of the shape remains the same regardless of how you rearrange the tiles, as long as you don't change the number or type of tiles used.
4-76: This problem asks you to simplify algebraic expressions using factoring and combining like terms.
Identify factors: Look for common factors in each term of the expression. For example, if you have 3x + 6y, you can factor out a 3.
Factor out the common factor: Rewrite the expression with the common factor outside the parentheses and the remaining terms inside.
Combine like terms: Once you have factored out the common factor, look for terms with the same variable and exponent. Add these terms together to simplify the expression further.
4-77: This problem requires analyzing a graph to determine if it represents a proportional relationship.
Proportional relationship: A proportional relationship means that asone variable increases or decreases, the other variable changes proportionally. This often results in a straight line on a graph.
Check for key features: Look for the following:
Constant ratio: The ratio between the changes in each variable should be constant. This means the same vertical change will always correspond to the same horizontal change, regardless of where you are on the graph.
Passes through the origin: A truly proportional relationship should pass through the point (0, 0).
Conclusion: Based on your observations, determine whether the graph represents a proportional relationship. If not, explain why not.
The probable question maybe:-
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