Question

1. Write an equation in point ­slope form for the line through the given point with the given slope. (–4, –2); m = -1/2

A. y + 2 = -1/2(x – 4)
B. y + 2 = (-1/2 ) x – 4
C. y + 2 = -1/2(x + 4)
D. y – 2 = -1/2(x – 4)

Answer 1

I hope this helps you

Answer 2

C. y + 2 = -1/2(x + 4)

`y = -(1)/(2)x -2 -2 = (1)/(2)x -4` Correct

Explanation:

For this case we have a point given
`P=(-4,-2)` and the slope for a line
`m = -(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 = -(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 = -(1)/(2)x -4`

We analyze one by one the options:

A. y + 2 = -1/2(x – 4)

`y = -(1)/(2) x +2 -2= (1)/(2)x` Incorrect

B. y + 2 = (-1/2 ) x – 4

`y = -(1)/(2)x -6` Incorrect

C. y + 2 = -1/2(x + 4)

`y = -(1)/(2)x -2 -2 = (1)/(2)x -4` Correct

D. y – 2 = -1/2(x – 4)

`y = -(1)/(2)x +2+2 = -(1)/(2)x +4` Incorrect