<em><u>Question:</u></em>
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
<em><u>Answer:</u></em>
Marty’s with a slope of 1/3 has the larger slope
<em><u>Solution:</u></em>
<em><u>Given that Marty equation is:</u></em>
![y + 3 = \frac{1}{3}(x+9)](https://tex.z-dn.net/?f=y%20%2B%203%20%3D%20%5Cfrac%7B1%7D%7B3%7D%28x%2B9%29)
<em><u>The point slope form is given as:</u></em>
![y - y_1 = m(x-x_1)](https://tex.z-dn.net/?f=y%20-%20y_1%20%3D%20m%28x-x_1%29)
Where, "m" is the slope of line
On comapring both equations,
![m = \frac{1}{3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B1%7D%7B3%7D)
<em><u>Ethan wrote a function:</u></em>
Consider any two values from the table we have;
(0, 10) and (2, 10.4)
<em><u>The slope is given by formula:</u></em>
![m = \frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
From above two points,
![(x_1, y_1) = (0, 10)\\\\(x_2, y_2) = (2, 10.4)](https://tex.z-dn.net/?f=%28x_1%2C%20y_1%29%20%3D%20%280%2C%2010%29%5C%5C%5C%5C%28x_2%2C%20y_2%29%20%3D%20%282%2C%2010.4%29)
Therefore,
![m = \frac{10.4-10}{2-0}\\\\m = \frac{0.4}{2} \\\\m = 0.2](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B10.4-10%7D%7B2-0%7D%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7B0.4%7D%7B2%7D%20%5C%5C%5C%5Cm%20%3D%200.2)
Thus we get,
![\text{Slope of Ethan} < \text{Slope of Marty}](https://tex.z-dn.net/?f=%5Ctext%7BSlope%20of%20Ethan%7D%20%3C%20%5Ctext%7BSlope%20of%20Marty%7D)
Therefore, Marty’s with a slope of 1/3 has the larger slope