1)what is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (−2, 4)?

2)what is the equation, in slope-intercept form, of the line that is perpendicular to the line
y – 4 = –2/3(x – 6) and passes through the point (−2, −2)?

1) 5x + 2y = 12
     5x - 12 = -2y
    /-2    /-2    /-2
   -2.5x + 6 = Y
  
   Slope is -2.5. You can make the equation Y = -2.5x + b.
   Plug in (-2,4) into that equation. it will make it parallel to the line. Solve for      B as well
  
   4 = -2.5(-2) + b
   4 = 5 + b
 -1 = b

Therefore, the line is Y = -2.5x - 1

2)  Y - 4 = -2(x-6)/3
     Y - 4 = -2x+12/3
 3(Y - 4) = -2x + 12
  3Y - 12 = -2x + 12
         3Y = -2x + 24
         /3       /3     /3
           Y = -2/3x + 8

Negative reciprocal. -2/3 = 3/2
This makes it perpendicular.

You can create this equation: Y = 3/2x + b
Plug in the point and solve for b.

 Y = 3/2x + b
-2 = 3/2(-2) + b
-2 = -3 + b
 1 = b

Therefore the line is Y = 3/2x + 1

Honestly, I have no clue if I did this right so :/

1) First, let's convert it to slope-intercept form to make it easier to work with:
5x + 2y = 12
2y = -5x + 12
y = -5/2x + 6

Now that we've got that, let's figure out where this new line's y-intercept is. First, we'll plug in the x and y coordinates:
4 = -5/2(-2) + b
4 = 5 + b
-1 = b
So the equation of our new line is y = -5/2x - 1
Let's get it back into general form:
y = -5/2x - 1
5/2x + y = -1
5x + 2y = -2

2) Let's get it into slope-intercept form:
4 = -2/3(6) + b
4 = -4 + b
8 = b
So we've got y = -2/3x + 8
The perpendicular line is pretty simple to find. Just use the inverse of the slope multiplied by -1. Let's solve for this one's y-intercept:
-2 = 3/2(-2) + b
-2 = -3 + b
1 = b
So the line is
y = 3/2x + 1