Use the point on the line and the slope of the line to determine whether any of the three additional points lies on the line. Point
Slope I: II: III:
A) Only point I lies on the line.
B) None of the points lies on the line.
C) Only point III lies on the line.
D) Only points I and II lie on the line.
E) Only points I and III lie on the line.

Question

Use the point on the line and the slope of the line to determine whether any of the three additional points lies on the line. Point
Slope   I:  II:  III: 
A) Only point I lies on the line. 
B) None of the points lies on the line. 
C) Only point III lies on the line. 
D) Only points I and II lie on the line. 
E) Only points I and III lie on the line.

Quizplus · Accepted Answer

Using the point-slope form of a line, we can write the equation of the line passing through the given point as:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is the given point on the line.
Substituting the given values, we get:
y - 3 = 2(x - 4)
Simplifying further, we get:
y - 3 = 2x - 8
y = 2x - 5
Now, substituting the x and y-coordinates of the three additional points into this equation, we can check whether they lie on the line or not.

For point I (3, -1), we have:
y = 2x - 5
-1 = 2(3) - 5
-1 = 1
This is false. Therefore, point I does NOT lie on the line.

For point II (2, -2), we have:
y = 2x - 5
-2 = 2(2) - 5
-2 = -1
This is false. Therefore, point II does NOT lie on the line.

For point III (5, 5), we have:
y = 2x - 5
5 = 2(5) - 5
5 = 5
This is true. Therefore, point III lies on the line.

Hence, the answer is A) Only point I lies on the line.

Use the Point on the Line and the Slope of the Line