Answer:
The value of k is 5.75
Explanation:
To find the value of k such that the line containing the points (-3, k) and (6, 10) is parallel to the line containing the points (5, 5) and (1, -2), you can start by determining the slope of the line passing through (5, 5) and (1, -2).
The slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:
m = (y₂ - y₁) / (x₂ - x₁)
For the line passing through (5, 5) and (1, -2):
m = (-2 - 5) / (1 - 5)
m = (-7) / (-4)
m = 7/4
Now, since the line you want to find is parallel to this line, it must also have the same slope. So, the slope of the line passing through (-3, k) and (6, 10) is also 7/4. We can now use this information to find k:
m = (10 - k) / (6 - (-3))
7/4 = (10 - k) / 9
Now, cross-multiply:
7 * 9 = 4 * (10 - k)
63 = 40 - 4k
Add 4k to both sides:
63 + 4k = 40
Subtract 40 from both sides:
4k = 63 - 40
4k = 23
Now, divide by 4:
k = 23 / 4
k = 5.75
So, the value of k is 5.75. The line containing the points (-3, 5.75) and (6, 10) will be parallel to the line containing the points (5, 5) and (1, -2).