Question

kenny wants to impress his teacher by finding an ordered pair that will result in a slope of $-\frac{5}{9}$ when given one ordered pair of (16, 9). he did the calculations two different ways, and got two different answers: (25, 4) and (7, 14). both ordered pairs gave him a slope of $-\frac{5}{9}$ when plugged back into the slope formula. he is nervous to show his teacher his answers. when kenny finally gets up the nerve to show his teacher the answers, she says,

both answers are correct. great job

\only (25, 4) is correct. great job!\

\only (7, 14) is correct. great job!\

\im sorry, but none of the answers are correct. i appreciate your attempt to answer the question. lets see where

Explanation:

Step1: Recall slope formula

The slope formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Given \((x_1,y_1)=(16,9)\) and slope \(m = -\frac{5}{9}\).

Step2: Check \((25,4)\)

Substitute \((x_2,y_2)=(25,4)\) into slope formula: \(\frac{4 - 9}{25 - 16}=\frac{-5}{9}=-\frac{5}{9}\).

Step3: Check \((7,14)\)

Substitute \((x_2,y_2)=(7,14)\) into slope formula: \(\frac{14 - 9}{7 - 16}=\frac{5}{-9}=-\frac{5}{9}\).

Answer:

Both answers are correct. Great job