Question 1: Option B: [tex]y=\frac{1}{3}x -2[/tex]
Question 2: Option D: [tex]y+1=3 (x+1)[/tex]
Solution:
Question 1:
The point on the given line are (2, 4) and (4, –2).
Slope of the given line:
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]$m=\frac{-2-4}{4-2}[/tex]
m = –3.
Slope of perpendicular line = –1 ÷ Slope of the given line
Slope of perpendicular line = [tex]\frac{1}{3}[/tex]
Perpendicular line passing through the point (3, 1).
Slope -intercept form using point slope formula,
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-1=\frac{1}{3} (x-3)[/tex]
[tex]y-1=\frac{1}{3} x-1[/tex]
[tex]y=\frac{1}{3}x -2[/tex]
Option B is the correct answer.
Question 2:
The point on the given line are (0, –3) and (2, 3).
Slope of the given line:
[tex]$m=\frac{3+3}{2-0}[/tex]
[tex]$m=\frac{6}{2}[/tex]
m = 3.
Slope of parallel lines are equal.
Slope of parallel line =3
parallel lines passing through the point (–1, –1).
Point slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y+1=3 (x+1)[/tex]
Option D is the correct answer.
