Answer:
C. y + 2 = -1/2(x + 4)
\(y = -\frac{1}{2}x -2 -2 = \frac{1}{2}x -4\) Correct
Step-by-step explanation:
For this case we have a point given \(P=(-4,-2)\) and the slope for a line \(m = -\frac{1}{2}\)
The general linear model is given by:
\(y= mx + b\)
For this case we have m given and we just need to find b, if we replace the info given we have this:
\(-2 = -\frac{1}{2} (-4) +b\)
And if we solve for b we got:
\(b = -2-2 = -4\)
So then our linear model is given by:
\(y = -\frac{1}{2}x -4\)
We analyze one by one the options:
A. y + 2 = -1/2(x – 4)
\(y = -\frac{1}{2} x +2 -2= \frac{1}{2}x\) Incorrect
B. y + 2 = (-1/2 ) x – 4
\(y = -\frac{1}{2}x -6\) Incorrect
C. y + 2 = -1/2(x + 4)
\(y = -\frac{1}{2}x -2 -2 = \frac{1}{2}x -4\) Correct
D. y – 2 = -1/2(x – 4)
\(y = -\frac{1}{2}x +2+2 = -\frac{1}{2}x +4\) Incorrect
