How do I find the slope of each of the three line segments 3,6,9 not on a straight line. then which two points is the slope the largest?
To find the slope of each line segment, we'll need to know the coordinates of the two points on each line. Let's assume the coordinates for the three line segments are as follows:
Line Segment 1:
Point A: (x1, y1) = (3, 2)
Point B: (x2, y2) = (6, 7)
Line Segment 2:
Point C: (x3, y3) = (6, 7)
Point D: (x4, y4) = (9, 4)
Line Segment 3:
Point E: (x5, y5) = (3, 2)
Point F: (x6, y6) = (9, 4)
Now, we can use the formula for slope (m) to calculate it for each line segment:
Slope of Line Segment 1:
m1 = (y2 - y1) / (x2 - x1)
= (7 - 2) / (6 - 3)
= 5 / 3
Slope of Line Segment 2:
m2 = (y4 - y3) / (x4 - x3)
= (4 - 7) / (9 - 6)
= -3 / 3
= -1
Slope of Line Segment 3:
m3 = (y6 - y5) / (x6 - x5)
= (4 - 2) / (9 - 3)
= 2 / 6
= 1 / 3
Now, to determine which two points have the largest slope, we compare the absolute values of the slopes:
|Slope of Line Segment 1| = |5/3| = 5/3
|Slope of Line Segment 2| = |-1| = 1
|Slope of Line Segment 3| = |1/3| = 1/3
From these comparisons, we can see that the largest slope is for Line Segment 1 (5/3), and the two points on Line Segment 1 (3, 2) and (6, 7) have the largest slope.
Therefore, the two points with the largest slope are (3, 2) and (6, 7).