Answer:
The types of slope for each pair are:
(2, 4) and (5, 1) => Negative
(3,5) and (-1,2) => Positive
(-7, 8) and (-7,0) => Undefined
(6.-3) and (4, -3) => Zero
Step-by-step explanation:
We will find the slope of each line to check the type of slope.
Slope is given by the formula:
![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)
Here (x1,y1) are the coordinates of first point and (x2,y2) are coordinates of second point
Now,
<u>(2, 4) and (5, 1)</u>
![m = \frac{1-4}{5-2} = \frac{-3}{3} =-1](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B1-4%7D%7B5-2%7D%20%3D%20%5Cfrac%7B-3%7D%7B3%7D%20%3D-1)
The slope is negative.
<u>(3,5) and (-1,2)</u>
![m = \frac{2-5}{-1-3} = \frac{-3}{-4} = \frac{3}{4}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B2-5%7D%7B-1-3%7D%20%3D%20%5Cfrac%7B-3%7D%7B-4%7D%20%3D%20%5Cfrac%7B3%7D%7B4%7D)
The slope is positive
(-7, 8) and (-7,0)
![m = \frac{0-8}{-7+7} = \frac{-8}{0}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B0-8%7D%7B-7%2B7%7D%20%3D%20%5Cfrac%7B-8%7D%7B0%7D)
division by zero makes the slope undefined.
(6.-3) and (4, -3)
![m=\frac{-3+3}{4-6} = \frac{0}{-2} = 0](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-3%2B3%7D%7B4-6%7D%20%3D%20%5Cfrac%7B0%7D%7B-2%7D%20%3D%200)
The slope is zero
Hence,
The types of slope for each pair are:
(2, 4) and (5, 1) => Negative
(3,5) and (-1,2) => Positive
(-7, 8) and (-7,0) => Undefined
(6.-3) and (4, -3) => Zero