Question

this situation can be modeled as a linear relationship.
complete the statement that describes the situation.
the drone is at a height of feet when leahs dad calls her in for lunch. the height of the drone decreases on its way to the ground.

Explanation:

Step1: Find the initial height

The y - intercept of the linear graph (when \(x = 0\), which represents the time when Leah's dad calls her in) is at \(y=35\). So the drone is at a height of 35 feet initially.

Step2: Calculate the rate of decrease (slope)

We can use two points on the line. Let's take \((0,35)\) and \((10,20)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{20 - 35}{10 - 0}=\frac{- 15}{10}=- 1.5\). This means the height decreases by 1.5 feet per second. We can also check with other points, for example, from \(x = 0\) to \(x = 3\), \(y\) goes from 35 to 30. The slope is \(\frac{30 - 35}{3-0}=\frac{-5}{3}\approx - 1.67\)? Wait, maybe a better pair. Let's take \((0,35)\) and \((6,26)\)? Wait, no, looking at the grid, at \(x = 3\), \(y = 30\); at \(x = 6\), \(y = 26\)? Wait, no, the first blank is the initial height, which is when \(x = 0\), so \(y = 35\). For the rate, let's take \((0,35)\) and \((10,20)\), the change in \(y\) is \(20 - 35=-15\), change in \(x\) is \(10 - 0 = 10\), so the rate of decrease is \(\frac{15}{10}=1.5\) feet per second. Alternatively, from \(x = 0\) to \(x = 2\), \(y\) is 35 to 32? Wait, maybe the grid lines: each x - unit is 1 second, each y - unit is 5 feet? Wait, no, the y - axis is height in feet, with 35 at \(x = 0\), 30 at \(x = 3\), 25 at \(x = 6\), 20 at \(x = 9\). So from \(x = 0\) to \(x = 3\) (3 seconds), \(y\) decreases by 5 feet. So the rate is \(\frac{5}{3}\approx1.67\)? Wait, no, maybe the first part is the initial height. The first blank: when \(x = 0\) (time when dad calls), the height is 35 feet. So the first answer is 35. For the second blank, the rate of decrease. Let's use two clear points: \((0,35)\) and \((10,20)\). The slope (rate of change) is \(\frac{20 - 35}{10-0}=\frac{-15}{10}=-1.5\), so the height decreases by 1.5 feet per second.

Answer:

The drone is at a height of \(\boldsymbol{35}\) feet when Leah's dad calls her in for lunch. The height of the drone decreases \(\boldsymbol{1.5}\) feet per second on its way to the ground. (Note: If we take other points, like from \(x = 0\) to \(x = 2\), \(y\) from 35 to 32 (change of - 3 over 2 seconds, rate - 1.5), so 1.5 feet per second is correct.)