Question

I will drop a picture

Answer 1

B) y= -1/2x -4

1) Let's start by picking two points from that line: (0,3) and (-2,-1). Now we can plug them into the slope formula and find out the slope of that line:

`m=(y_2-y_1)/(x_2-x_1)\Rightarrow m=(-1-3)/(-2-0)=(-4)/(-2)=2`

2) Examining that graph we can see that when x=0 y=3, so the linear coefficient b is 3. Therefore we can write the equation as y= 2x-3.

2.2) Since the question wants a perpendicular line, then the slope of this perpendicular line must be reciprocal and opposite to m=2, so:

`m\perp=-(1)/(2)`

So, plugging the given point (6,-7) we can find out the linear coefficient of that perpendicular line:

y=mx +b

-7 = 6(-1/2) +b

-7 =-3 +b

-7+3 = b

b=-4

3) Hence, the answer is y= -1/2x -4