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
Answer:
Marty’s with a slope of 1/3 has the larger slope
Solution:
Given that Marty equation is:
[tex]y + 3 = \frac{1}{3}(x+9)[/tex]
The point slope form is given as:
[tex]y - y_1 = m(x-x_1)[/tex]
Where, "m" is the slope of line
On comapring both equations,
[tex]m = \frac{1}{3}[/tex]
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:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
From above two points,
[tex](x_1, y_1) = (0, 10)\\\\(x_2, y_2) = (2, 10.4)[/tex]
Therefore,
[tex]m = \frac{10.4-10}{2-0}\\\\m = \frac{0.4}{2} \\\\m = 0.2[/tex]
Thus we get,
[tex]\text{Slope of Ethan} < \text{Slope of Marty}[/tex]
Therefore, Marty’s with a slope of 1/3 has the larger slope
Answer:
C
Step-by-step explanation:
Marty’s with a slope of 1/3 has the larger slope
