Question 945144
Lines with equal slopes are parallel, so put the equations in slope intercept form (y=mx+b, m is the slope)
y=3x+10 This equation is in correct form, and has a slope=3
12x – 3y = –36 Add 3y to each side
12x=3y-36 Add 36 to each side
12x+36=3y Divide each side by 3
4x+12=y Reverse sides of equation for clarity
y=4x+12  This equation has slope=4, which is not parallel to a line with slope=3
ANSWER No, the lines are not parallel.
{{{ graph( 500, 500, -10, 10, -10, 10, 3x+10, 4x+12) }}}
---OR--- 
If the lines have a common solution, they intersect and therefore are not parallel
Solve each equation for y and set the two equal (we've solved for y above)
y=3x+10
y=4x+12
3x+10=4x+12 Subtract 3x from each side
10=x+12 Subtract 12 from each side
-2=x
y=3(-2)+10
y=4
(-2,4) is a solution to this equation
12x-3y=-36
12(-2)-3(4)=-36
-24-12=-36
-36=-36
(-2.4) is also a solution to this equations, so the lines intersect,thus they are NOT parallel