Question

The points (−1,r) and (4,4) lie on a line with slope −2. Find the missing coordinate r.

Answer 1

interesting

Answer 2

We can use this equation here \[y-y_{1} = m(x-x_{1})\]

r = y1

then we solve for y1

\[y_{1} = y-m(x-x_{1})\]

plug in everything


\[4-(-2)*(4-(-1)) = 4-(-2*5) = 14\]

this means that y_{1} = 14 = r

now let's check this

(-1,14)
(4,4)

\[m = \frac{ y-y_{1} }{ x-x_{1} } = \frac{ 14-4 }{ -1-4 } = \frac{ 10 }{ -5 } = -2 \]

Answer 3

Refer to the Mathematica attachment.