Marty and Ethan both wrote a function, but in different ways. Marty
y plus 3 equals StartFraction 1 Over 3 EndFraction left-parenthesis x plus 9 right-parenthesis.

Ethan

A two column table with 5 rows. The first column, x, has the entries, negative 4, negative 2, 0, 2. The second column, y, has the entries, 9.2, 9.6, 10, 10.4.

Whose function has the larger slope?

Marty's function has larger slope as compared to Ethan's slope.

Step-by-step explanation:

Marty function:

y plus 3 equals StartFraction 1 Over 3 EndFraction left-parenthesis x plus 9 right-parenthesis.

Writing in mathematical form:

Marty has written expression in point-slope form: where m is slope

So, comparing Marty's equation with general point-slope form equation we get slope

Now, Ethan has a table

x        y

-4      9.2

-2      9.6

0       10

2       10.4

We can find slope using formula:

Using any two points, we can find slope of Ethan's equation

So, we get Marty's slope = 0.3

Ethan's slope = 0.2

So, Marty's function has larger slope as 0.3 is greater than 0.2