Question

A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally. A piece of climbing equipment at a gym is 10 feet high and extends 6 feet horizontally. Which statement best compares the slopes of the two pieces of equipment?

Answer 1

Answer: The comparison is mentioned below.

Step-by-step explanation:

A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally.

Therefore its slope = length of the equipment vertically / length of equipment horizontally

$m_1$=  6/4 = 3/2 = 1.5

And, A piece of climbing equipment at a gym is 10 feet high and extends 6 feet horizontally.

Therefore slope, $m_2$=  10/6 = 5/3=1.67 (approx)

Since, $m_1$<$m_2$

Thus the slope of equipment first is less than slope of second equipment.

Answer 2

You can use the definition of slope which is height increased per base length given.

The statement that compares the slopes of two pieces of equipment is

Slope of first climbing equipment = 3/2 < slope of second climbing equipment = 5/3

What is the slope of a straight line?

Slope tells how vertical a line is.

The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.

To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.

This is because the more the height of the line to thee amount we walk or run on the horizontal axis, the more the slope is. That's why we took difference of horizontal axis in denominator and difference of vertical axis on numerator.

Formula for slope, thus, is;

(went from $x_1$ to $x_2$ and found that line goes from  $y_1$ to $y_2$  vertically)

where

$(x_1,y_1) , (x_2, y_2)$

are two points on the considered line.

Using the above formula, we get the slopes as:

For first climbing equipment rise = 6 feet, run(horizontal) = 4 feet

Thus, slope = $\dfrac{6}{4} = \dfrac{3}{2} \approx 1.5$

For second climbing equipment rise = 10 feet, run(horizontal) = 6 feet

Thus, slope=  $\dfrac{10}{6} = \dfrac{5}{3} \approx 1.6\overline{6}$

Thus,

Slope of first climbing equipment = 3/2 < slope of second climbing equipment = 5/3

Learn more about slopes here:

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