Respuesta :
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) = [tex]-\frac{3}{5}[/tex]
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 [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is given as:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Now, the slope of a line passing through (-8, 8) and (2, 2) is given as:
[tex]m_1=\frac{2-8}{2-(-8)}=\frac{-6}{10}=-\frac{3}{5}[/tex]
So, [tex]m=m_1[/tex]
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:
[tex]m_2=\frac{2-(-1)}{0-(-5)}=\frac{3}{5}[/tex]
So, [tex]m\ne m_2[/tex]
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:
[tex]m_3=\frac{-9-6}{6-(-3)}=\frac{-15}{9}=-\frac{5}{3}\ne m[/tex]
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:
[tex]m_4=\frac{-2-1}{3-(-2)}=-\frac{3}{5}=m[/tex]
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:
[tex]m_5=\frac{5-2}{5-0}=\frac{3}{5}\ne m[/tex]
Therefore, option (E) is not correct.
Hence, only options (A) and (D) are correct.
