# (2,3), (3,-2) and (8,k). find k

Asked on by studius

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

What is your question?

Let's suppose that you want to determine k when the points are on the same line.

First, we'll determine the line taht is passing through the points (2,3) and (3,-2):

y = ax + b

If (2,3) is on the line, then it's coordinates verify the equation of the line:

3 = 2a + b => b = 3 - 2a (1)

If (3,-2) is on the line, then it's coordinates verify the equation of the line:

-2 = 3a + b (2)

We'll substitute (1) in (2) and we'll get:

-2 = 3a + 3 - 2a

-2 - 3 = 3a - 2a

-5 = a

a = -5

b = 3 - 2a => b = 3 + 10 = 13

The equation of the line that is passing through (2,3) and (3,-2) is:

y = -5x + 13

Now, we'll impose the constraint that this line to pass through the point (8,k), too:

k = -5*8 + 13

k = -40 + 13

k = -27

The line is passing through all these given points, for k = -27.

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