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 with a slope of 2/3
Ethan’s with a slope of 2/5
Marty’s with a slope of 1/3
Ethan’s with a slope of 1/5

Question:

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

Marty

y+3=1/3(x+9)

Ethan

x y

-4 9.2

-2 9.6

0 10

2 10.4

Whose function has the larger slope?

1. Marty’s with a slope of 2/3

2. Ethan’s with a slope of 2/5

3. Marty’s with a slope of 1/3

4. Ethan’s with a slope of 1/5

Marty’s with a slope of 1/3 has the larger slope

Solution:

Given that Marty equation is:

The point slope form is given as:

Where, "m" is the slope of line

On comapring both equations,

Ethan wrote a function:

Consider any two values from the table we have;

(0, 10) and (2, 10.4)

The slope is given by formula:

From above two points,

Therefore,

Thus we get,

Therefore, Marty’s with a slope of 1/3  has the larger slope