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: [tex]y=mx+b[/tex] ....[1]
where,
m is the slope and b is the y-intercept.
Formula for Slope is given by:
[tex]\text{Slope} = \frac{y_2-y_1}{x_2-x_1}[/tex] ....[2]
As per the statement:
Marty and Ethan both wrote a function, but in different ways.
Marty equation is:
[tex]y+3 = \frac{1}{3}(x+9)[/tex]
using distributive property [tex]a \cdot(b+c) = a\cdot b + a\cdot c[/tex] we have;
[tex]y+3 = \frac{1}{3}x+3[/tex]
Subtract 3 from both sides we have;
[tex]y= \frac{1}{3}x[/tex]
On comparing with [1] we have;
Slope of Marty = [tex]\frac{1}{3}=0.333..[/tex]
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;
[tex]\text{Slope} = \frac{10.4-10}{2-0}=\frac{0.4}{2} =0.2[/tex]
Slope of Ethan = 0.2
[tex]\text{Slope of Ethan} < \text{Slope of Marty}[/tex]
Therefore, . Marty’s with a slope of 1/3 function has the larger slope
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
