Determine the equation of the line that is PERPENDICULAR to the line
$y equals negative 1 divided by 4 x plus 1 divided by 12$ and contains the point (-2, 6).

$y = 4 x + 6$
$y = 4 x + 14$
$y = 3 x + 12$
$y = - 1 / 4 x + 11 / 2$

hint Hint:

$W e space k n o w space t h a t space t w o space p e r p e n d i c u l a r space l i n e space s l o p e space m u l t i p l i c a t i o n space i s space minus 1 s o space m subscript 1 cross times m subscript 2 space equals space minus 1$

The correct answer is: $y equals 4 x plus 14$

$y space equals space 4 x space plus space 14 comma space i s space t h e space c o r r e c t space c h o i c e g i v e n space l i n e space L subscript 1 space end subscript colon y space equals space minus 1 fourth x space plus space 1 over 12 c o m p a r e space t h e space g i v e n space l i n e space w i t h space space y space equals space m x space plus space c comma space t o space f i n d space t h e space s l o p e s o space s l o p e space o f space t h e space g i v e n space l i n e space m subscript 1 space equals space minus 1 fourth w e space h a v e space t o space f i n d space a space l i n e left parenthesis L subscript 2 right parenthesis space w h i c h space i s space p e r p e n d i c u l a r space t o space g i v e n space l i n e W e space k n o w space t h a t space t w o space p e r p e n d i c u l a r space l i n e space s l o p e space m u l t i p l i c a t i o n space i s space minus 1 s o space m subscript 1 cross times m subscript 2 space equals space minus 1 m subscript 2 cross times negative 1 fourth space equals negative 1 s o space m subscript 2 space equals space 4 a l s o space l i n e space L subscript 2 space end subscript p a s s e s space t h r o u g h space left parenthesis space minus 2 comma space 6 right parenthesis y space equals space m subscript 2 x plus space c 6 space equals space 4 space cross times space left parenthesis negative 2 right parenthesis space plus space c c space equals space 6 plus 8 c equals space 14 s o space t h e space l i n e space L subscript 2 space colon space y space equals space 4 x space plus space 14 comma space i s space t h e space c o r r e c t space a n s w e r$

Calculate the slope of the following 12x - 6y = 30.

In mathematics, the equation of a straight line describes the relationship between the coordinate points that comprise that line. It can be expressed in several ways and contains information about a line's slope, x-intercept, and y-intercept.
A straight line's standard form is given by the equation ax + by = c, where a, b, and c are real numbers. Let's illustrate how to put the equation y = 3x - 1 in standard form. Add 2x to neither side of the equation, and we get
y - 3x = 3x - 1 - 3x
= y - 3x = -1
= 3x - y = 1
As a result, we arrive at the line's standard form, which is 3x - y = 1