Question

Select all of the situations that represent a linear relationship between x and y.
the total area, in square meters, y, of a square garden if the side length is x meters
the height, y, of a 6-foot tree that grows 0.2 feet per month for x months
the total cost, y, of a ski rental from a company that charges $15 plus an additional $8 per day rented for x days
the total miles, y, traveled by a car going 62 miles per hour in x hours

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Linear relationship always produces a straight line and are without exponential.

Lets check all the given options:

1. the total area, in square meters, y, of a square garden if the side length is x meters.

The area of a square is $(side)^{2}$

Here, side is 'x' and area 'y' will be $x^{2}$.

This is not linear.

2. the height, y, of a 6-foot tree that grows 0.2 feet per month for x months

The equation forms:

$y=6+0.2x$

When x = 1

$y=6.2$

When x = 2

$y=6+0.2(2)$

=> $y=6.4$

When x = 3

$y=6+0.2(3)$

=> $y=6.6$

This is a linear relation.

3. the total cost, y, of a ski rental from a company that charges $15 plus an additional $8 per day rented for x days

The equation forms:

$y=15+8x$

When x = 1

$y=15+8=23$

When x = 2

$y=15+8(2)$

=> $y=31$

When x = 3

$y=15+8(3)$

=> $y=39$

This is also linear.

4. the total miles, y, traveled by a car going 62 miles per hour in x hours

The equation forms:

$y=62x$

When x = 1

$y=62$

When x = 2

$y=62(2)$

=> $y=124$

When y = 3

$y=62(3)$

=> $y=186$

This is also linear in nature.