Question

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

Answer 1

Answer:

Option 3 is correct

Marty’s with a slope of 1/3

Step-by-step explanation:

Using slope intercept form:

The equation of line is: $y=mx+b$          ....[1]

where,

m is the slope and b is the y-intercept.

Formula for Slope is given by:

$\text{Slope} = \frac{y_2-y_1}{x_2-x_1}$         ....[2]

As per the statement:

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

Marty equation is:

$y+3 = \frac{1}{3}(x+9)$

using distributive property $a \cdot(b+c) = a\cdot b + a\cdot c$ we have;

$y+3 = \frac{1}{3}x+3$

Subtract 3 from both sides we have;

$y= \frac{1}{3}x$

On comparing with [1] we have;

Slope of Marty = $\frac{1}{3}=0.333..$

Ethan wrote a function:

Consider any two values from the table we have;

(0, 10) and (2, 10.4)

Substitute these in [2] we have;

$\text{Slope} = \frac{10.4-10}{2-0}=\frac{0.4}{2} =0.2$

Slope of Ethan = 0.2

$\text{Slope of Ethan} < \text{Slope of Marty}$

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

Answer 2

Answer:

Marty’s with a slope of 1/3

Step-by-step explanation:

Marty

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

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

y = (1/3)*x

Marty's slope: 1/3

To calculate Ethan’s slope we use the following formula :

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are points of the function. Replacing with points (0,10) and (2, 10.4) we get:

m = (10.4 - 10)/(2 - 0) = 1/5

Ethan’s slope: 1/5