Question

Marty and Ethan both wrote a function, but in different ways.

Answer 1

Answer:

Marty's with a slope of 1/3

Step-by-step explanation:

The functions Marty and Ethan wrote are analyzed the find the slope of each of the function

The equation Marty wrote is presented here as follows;

$y + 3 = \dfrac{1}{3} \cdot\left (x + 9 \right)$

Marty's equation can be written in slope and intercept form, y = m·x + c, as follows;

$y = \dfrac{1}{3} \cdot\left (x + 9 \right) - 3$

$y = \dfrac{1}{3} \cdot x + \dfrac{9}{3} \right) - 3 = \dfrac{1}{3} \cdot x + 0$

$y = \dfrac{1}{3} \cdot x$

By comparison, the slope of the function, m = 1/3

$\therefore \ the \ slope \ of \ Marty's \ function, \ y + 3 = \dfrac{1}{3} \cdot\left (x + 9 \right), \ m =\dfrac{1}{3}$

Marty's function has a slope of m = 1/3

Ethan has the following two column table;

$\begin{array}{rl}x&y\\-4&9.2\\-2&9.6\\0&10\\2&10.4\end{array}$

The slope, m, of the data in the above table is given as follows;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Taking any two points, (x₁, y₁) = (-4, 9.2), and (x₂, y₂) = (2, 10.4), we get;

$Slope, \, m =\dfrac{10.4-9.2}{2-(-4)} = \dfrac{1.2}{6} = \dfrac{1}{5}$

Ethan's function has a slope of m = 1/5

Therefore;

Marty's slope of 1/3 is larger, given that 1/3 > 1/5.