Answer:
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: [tex]y+3=\frac{1}{3}(x+9)[/tex]
Marty has written expression in point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where m is slope
So, comparing Marty's equation with general point-slope form equation we get slope [tex]m=\frac{1}{3}\:or\: 0.3[/tex]
Now, Ethan has a table
x y
-4 9.2
-2 9.6
0 10
2 10.4
We can find slope using formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using any two points, we can find slope of Ethan's equation
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{9.6-9.2}{-2-(-4)} \\Slope=\frac{0.4}{-2+4} \\Slope=\frac{0.4}{2} \\Slope=0.2[/tex]
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
