Explanation:
The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
slope = (y2 - y1)/(x2 - x1)
In this case, the two points on the line k are (-4, 3) and (2, -1). Using the formula above, we can calculate the slope of k as:
slope = (-1 - 3)/(2 - (-4)) = (-4)/6 = -2/3
Therefore, the slope of line k is -2/3.
To write a ratio expressing the slope of k, we can choose any two different values of x and y that are on the line k, and write the ratio of the change in y to the change in x. Let's choose the two points (2, -1) and (-4, 3) again.
The change in y between these two points is:
-1 - 3 = -4
The change in x between these two points is:
2 - (-4) = 6
Therefore, the ratio of the change in y to the change in x is:
-4/6 = -2/3
This is the same as the slope of line k that we calculated earlier. So the ratio expressing the slope of k is -2/3.