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Find the value of k when the points (1,4), 6-3, 16) and (k, -2) lie in one straight line​

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Final answer:

To find the value of k when the points (1,4), (6,-3), and (16,k) lie on a straight line, we can calculate the slope between (1,4) and (6,-3). Then, we can set up an equation using the slope between (6,-3) and (16,k) and solve for k. The value of k is -17.

Step-by-step explanation:

To determine the value of k when the points (1,4), (6,-3), and (16,k) lie on a straight line, we can use the concept of slope. The slope between two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

Let's calculate the slope between the points (1,4) and (6,-3):

slope = (-3 - 4) / (6 - 1) = -7/5

Since the points (1,4), (6,-3), and (16,k) must lie on the same line, the slope between the points (6,-3) and (16,k) should also be -7/5. We can use this information to find the value of k:

-7/5 = (k - (-3)) / (16 - 6)

After simplifying, we get:

-7/5 = (k + 3) / 10

Cross multiplying:

-70 = 5k + 15

Subtracting 15 from both sides:

-85 = 5k

Dividing both sides by 5:

k = -17

User Gary Hellman
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