The points option A) (4,-5) and option C) (2,1) lies on the line m.
Step-by-step explanation:
The given equation of the line is [tex]y = (-2/3)x + 8[/tex]
The general equation of the line is [tex]y=mx+b[/tex]
where,
- m is the slope of the line.
- b is the y-intercept of the line.
From the given equation,
It can be found that the slope of the line, m is -2/3.
The line is parallel to the given line. Therefore, their slopes are equal.
Since the two lines are parallel, their slope is also same.
The line passes through the point (-1,3).
To find the slope :
Slope = [tex](y2-y1)/(x2-x1)[/tex]
Now, let's check the each options to find the slope is same or not.
Option A) is (-4,5) and the given point is (-1,3)
Slope = [tex](3-5)/(-1+4)[/tex]
⇒ slope = -2/3
Therefore, the point (-4,5) could also be on the line m.
Option B) is (-3,6) and the given point is (-1,3)
Slope = [tex](3-6)/(-1+3)[/tex]
⇒ slope = -3/2
The point (-3,6) cannot be on the line m.
Option C) is (2,1) and the given point is (-1,3)
Slope = [tex](3-1)/(-1-2)[/tex]
⇒ slope = -2/3
Therefore, the point (2,1) could also be on the line m.
Option D) is (3,-2) and the given point is (-1,3)
Slope = [tex](3+2)/(-1-3)[/tex]
⇒ slope = -5/4
The point (3,-2) cannot be on the line m.
Option E) is (6,-3) and the given point is (-1,3)
Slope = [tex](3+3)/(-1-6)[/tex]
⇒ slope = -6/7
The point (6,-3) cannot be on the line m.
