The question is missing the options. The options are:
(A) (-8, 8) and (2, 2)
(B) (-5, -1) and (0, 2)
(C) (-3, 6) and (6.-9)
(D) (-2, 1) and (3,-2)
(E) (0, 2) and (5,5)
Answer:
Options (A) and (D)
Step-by-step explanation:
Given:
A line with slope (m) = ![-\frac{3}{5}](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B5%7D)
Now, a parallel line to the given line will have the same slope.
So, let us check each of the given options.
Option (A)
(-8, 8) and (2, 2)
The slope of line passing through two points
is given as:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Now, the slope of a line passing through (-8, 8) and (2, 2) is given as:
![m_1=\frac{2-8}{2-(-8)}=\frac{-6}{10}=-\frac{3}{5}](https://tex.z-dn.net/?f=m_1%3D%5Cfrac%7B2-8%7D%7B2-%28-8%29%7D%3D%5Cfrac%7B-6%7D%7B10%7D%3D-%5Cfrac%7B3%7D%7B5%7D)
So, ![m=m_1](https://tex.z-dn.net/?f=m%3Dm_1)
Therefore, option (A) is correct.
Option (B): (-5, -1) and (0, 2)
The slope of a line passing through (-5, -1) and (0, 2) is given as:
![m_2=\frac{2-(-1)}{0-(-5)}=\frac{3}{5}](https://tex.z-dn.net/?f=m_2%3D%5Cfrac%7B2-%28-1%29%7D%7B0-%28-5%29%7D%3D%5Cfrac%7B3%7D%7B5%7D)
So, ![m\ne m_2](https://tex.z-dn.net/?f=m%5Cne%20m_2)
Therefore, option (B) is not correct.
Option (C): (-3, 6) and (6, -9)
The slope of a line passing through (-3, 6) and (6, -9) is given as:
![m_3=\frac{-9-6}{6-(-3)}=\frac{-15}{9}=-\frac{5}{3}\ne m](https://tex.z-dn.net/?f=m_3%3D%5Cfrac%7B-9-6%7D%7B6-%28-3%29%7D%3D%5Cfrac%7B-15%7D%7B9%7D%3D-%5Cfrac%7B5%7D%7B3%7D%5Cne%20m)
Therefore, option (C) is not correct.
Option (D): (-2, 1) and (3, -2)
The slope of a line passing through (-2, 1) and (3, -2) is given as:
![m_4=\frac{-2-1}{3-(-2)}=-\frac{3}{5}=m](https://tex.z-dn.net/?f=m_4%3D%5Cfrac%7B-2-1%7D%7B3-%28-2%29%7D%3D-%5Cfrac%7B3%7D%7B5%7D%3Dm)
Therefore, option (D) is correct.
Option (E): (0, 2) and (5, 5)
The slope of a line passing through (0, 2) and (5, 5) is given as:
![m_5=\frac{5-2}{5-0}=\frac{3}{5}\ne m](https://tex.z-dn.net/?f=m_5%3D%5Cfrac%7B5-2%7D%7B5-0%7D%3D%5Cfrac%7B3%7D%7B5%7D%5Cne%20m)
Therefore, option (E) is not correct.
Hence, only options (A) and (D) are correct.