Question

A line contains the points (-1,k), (6,k-1), and (20,3).
What is the value of k?

Answer 1

u can answer, but i have to go eat dinner right now so please don't feel like I'm not listening. Please answer if you know, will give medal

Answer 2

Label the 3 points A,B,C
So
A = (-1,k)
B = (6,k-1)
C = (20,3)

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Step 1) find the expression for the slope of the line through A and C
\[\Large m = \frac{y_2 - y_1}{x_2 - x_1}\]
\[\Large m = \frac{3-k}{20-(-1)}\]
\[\Large m = \frac{3-k}{20+1}\]
\[\Large m = \frac{3-k}{21}\]
So the slope expression for the line through A and C is \(\Large \frac{3-k}{21}\)

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Step 2) find the expression for the slope of the line through B and C
\[\Large m = \frac{y_2 - y_1}{x_2 - x_1}\]
\[\Large m = \frac{3-(k-1)}{20-6}\]
\[\Large m = \frac{3-k+1}{14}\]
So the slope expression for the line through B and C is \(\Large \frac{3-k+1}{14}\)

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Step 3) equate the two slope expressions from step 1) and step 2)
\[\Large \frac{3-k}{21}=\frac{3-k+1}{14}\]


I'll let you solve for k

Answer 3

okay thank you very much
@jim_thompson5910

Answer 4

you always give the best explanations and answers

Answer 5

glad to be of help

Answer 6

:)

Answer 7

@jim_thompson5910
does k = 6?

Answer 8

yep you nailed it

Answer 9

not really, it took me too long, but thank you :)

Answer 10

you're welcome