Question 1197981
.
What is the gradient of the lines with the equation
3y+6x=12
12x-4y-3=0
~~~~~~~~~~~~~~~~~~



<pre>
For a line defined by a linear function, gradient is the same as (is the synonym of) the slope.


Therefore, the gradient of the first line,  3y + 6x = 12,  is -2,
since from the equation  (a)  3y = 12 - 6x,  or  y = -2x + 4  with the slope of -2.


The gradient of the second line,  12x - 4y - 3  = 0,  is 3,
since from the equation  (b)  4y = 12x - 3,  or  y = 3x - (3/4)  with the slope of 3.
</pre>

Solved and explained.


------------------


The wording in your post is INCORRECT.


The correct wording is as follows:


<pre>
    What are the gradients of the lines with equations
        (a)  3y + 6x    = 12
        (b) 12x - 4y -3 =  0
</pre>

Your incorrect wording in the post reflects your incorrect thinking - 
- so be careful and accurate, &nbsp;when you compose/write/post/publish problems in &nbsp;Math &nbsp;(&nbsp;!&nbsp;)


Or consider to hire an assistant/(an expert)/(a professor), who will edit your writing after you . . .