In the coordinate plane, line L passes above the points (50, 70) and (100, 89) but below the point (80, 84). Which of the following could be the slope of line L?

Question

In the coordinate plane, line L passes above the points (50, 70) and (100, 89) but below the point (80, 84).  Which of the following could be the slope of line L?

Vinod · Accepted Answer

let's understand what the question is telling us:Line L passes above (50, 70) and (100, 89)Line L passes below (80, 84)
We can use these points to establish a range for the slope of line L.
Let's calculate the slope between (50, 70) and (100, 89):Slope = (y2 - y1) / (x2 - x1)= (89 - 70) / (100 - 50)= 19 / 50= 0.38
This slope of 0.38 is a lower bound for our line L, because L must pass above both these points.
Now, let's calculate the slope between (50, 70) and (80, 84):Slope = (84 - 70) / (80 - 50)= 14 / 30&asymp; 0.4667
This slope of approximately 0.4667 is an upper bound for our line L, because L must pass below (80, 84).
Therefore, the slope of line L must be greater than 0.38 but less than 0.4667.
We can write this as an inequality:0.38 < slope of L < 0.4667
Now, we need to check which of the given options falls within this range.
Therefore, any value between 0.38 and 0.4667 could be the slope of line L.