If (y=34+8x), what will be the total increase in (y) from (x=1) to (x=6)?
Answer and explanation
Correct answer: (40)
The expression \\(y=34+8x\\) is a linear rule. Its coefficient of \\(x\\), namely 8, tells us that \\(y\\) increases by 8 whenever \\(x\\) increases by 1. We need the total change, not the value of \\(y\\) at just one endpoint. From \\(x=1\\) to \\(x=6\\), the change in \\(x\\) is \\(6-1=5\\).
Multiplying the constant rate by this change gives the increase: \\(8\times5=40\\). Directly, \\(y(1)=34+8=42\\) and \\(y(6)=34+48=82\\), so the difference is \\(82-42=40\\) as well. The constant term 34 cancels when finding a difference. Hence option B, 40, is correct; 48 would incorrectly use the endpoint value of the variable part without accounting for the starting point.
Frequently asked questions
What is the correct answer to this question?
(40)
Why is this the correct answer?
The expression \\(y=34+8x\\) is a linear rule. Its coefficient of \\(x\\), namely 8, tells us that \\(y\\) increases by 8 whenever \\(x\\) increases by 1. We need the total change, not the value of \\(y\\) at just one endpoint. From \\(x=1\\) to \\(x=6\\), the change in \\(x\\) is \\(6-1=5\\).
Multiplying the constant rate by this change gives the increase: \\(8\times5=40\\). Directly, \\(y(1)=34+8=42\\) and \\(y(6)=34+48=82\\), so the difference is \\(82-42=40\\) as well. The constant term 34 cancels when finding a difference. Hence option B, 40, is correct; 48 would incorrectly use the endpoint value of the variable part without accounting for the starting point.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear growth and decay.
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