which cannot be represented by a linear function?
A. The area of a square, given its side length
B. the price of fruit, given the weight of the fruit
C. The number of steps on a ladder, given the height
D. The number of inches,given the number of yards
I think it is C.
Thank you.
Thank You.
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NO !!!
A = length^2
quadratic, not linear
so A, area of square, is NOT linear in length of side
To determine which of the given options cannot be represented by a linear function, we need to understand what a linear function is.
A linear function is a mathematical function that can be represented by a straight line on a graph. It follows the form y = mx + b, where x and y are variables, m is the slope, and b is the y-intercept.
Now, let's evaluate each option to see if it can be represented by a linear function:
A. The area of a square, given its side length:
The area of a square is determined by multiplying its side length by itself. Since multiplication is a non-linear operation (not a straight line on a graph), the area of a square cannot be represented by a linear function.
B. The price of fruit, given the weight of the fruit:
The relationship between the weight of fruit and its price can vary depending on factors like supply, demand, and pricing strategies. It is unlikely that the price of fruit could be represented by a linear function since it does not follow a straight line pattern.
C. The number of steps on a ladder, given the height:
The relationship between the number of steps on a ladder and its height can be easily represented by a linear function. As the height increases, the number of steps also increases, and this relationship can be represented by a straight line on a graph. Therefore, C is not the correct answer.
D. The number of inches, given the number of yards:
Since there are 36 inches in a yard, the relationship between the number of inches and the number of yards can be represented by a linear function. It follows a consistent pattern, making it possible to represent with a straight line on a graph.
Based on our analysis, option A (the area of a square, given its side length) cannot be represented by a linear function. Therefore, the correct answer is A, not C.