Question

18. A line has slope = -9 and goes through the point (-4,-2). What is the equation of this line in point-slope forma A. y + 2 = -91X - 4) B. Y-2= -9(x-4) C. y 2 = -91x + 4) D. y - 2= -9(x +4)

Answer 1

The straight line equation is

$y=mx+b$

where m is the slope and b the y-intercept. In our case m=-9. Hence, our line

equations has the form

$y=-9x+b$

In order to find b, we must use the given point (-4,-2) and substitute it and the last equation.

It yields,

$-2=-9(-4)+b$

hence, we have

$\begin{gathered} -2=36+b \\ -2-36=b \\ b=-38 \end{gathered}$

Finally, the answer is

$y=-9x-38$

Now, we can rewrite this equation as

$\begin{gathered} y=-9(x+4)-2 \\ \text{which is equal to} \\ y+2=-9(x+4) \end{gathered}$

then, the answer is C.