Complete Question:
The slope between A and B is ⅗.The slope between points B and C is 6/10. Antoine says all three of these points are on the same line. What statement is true?
A) Antoine is correct because both slopes are equal to ⅗.
B) Antoine is incorrect because the slope of a line is always greater than 1.
C) Antoine is incorrect because the slope is the same between any two points on a line.
D) Antoine is correct because the slope is not the same between any two points on a line
Answer:
A) Antoine is correct because both slopes are equal to ⅗.
Explanation:
We are given that:
Slope between A and B = ⅗
Slope between B and C = ⁶/10
If we reduce the fraction, ⁶/10 further, we would have: (2*3)/(2*5) = ³/5.
Therefore, slope between A and B, and slope between B and C would be the same = ⅗.
Since the slope are the same, it implies that all three points are in the same line.
Therefore, Antoine is correct.