compare the two quantities and determine whether the first one is the greatest, the second is the greatest, the two are equal, or the relationship cannot be determined from the information given...
1st: the slope of the line that contains A(2,4) and B(-1,3)
2nd: the slope of the line that contains C(-2,1) and D(5,3)
To compare the two quantities, we need to calculate the slopes of the lines that contain the given points. The slope of a line can be found using the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
Let's start with the first quantity:
1st: the slope of the line that contains A(2,4) and B(-1,3)
The change in y-coordinates = 3 - 4 = -1
The change in x-coordinates = -1 - 2 = -3
So, the slope of the line passing through points A and B is: slope1 = (-1) / (-3) = 1/3.
Now, let's move on to the second quantity:
2nd: the slope of the line that contains C(-2,1) and D(5,3)
The change in y-coordinates = 3 - 1 = 2
The change in x-coordinates = 5 - (-2) = 7
So, the slope of the line passing through points C and D is: slope2 = 2 / 7.
To determine the relationship between the two quantities, we can compare the values of slope1 and slope2.
If slope1 > slope2, then the first quantity (slope of the line through A and B) is the greatest.
If slope1 < slope2, then the second quantity (slope of the line through C and D) is the greatest.
If slope1 = slope2, then the two quantities are equal.
If the relationship between the slopes cannot be determined based on the given information, it means that the slopes are not directly related to each other.
Now, you can compare the values of slope1 and slope2 to determine the relationship between the two quantities.