Hello there!
To find the slope of the line 3x+7y=10 you can change it to slope intercept form or do implicit differentiation.
3x+7y=10
d/dx[3x+7y]=d/dx[10]
d/dx[3x]+d/dx[7y]=d/dx[10]
3+7dy/dx=0
7dy/dx=-3
dy/dx(7)=-3
dy/dx=-3/7
The slope of this line is -3/7
Since the lines are parallel, the equation of our line will look like:
y=(-3/7)x+b
Now to find b, use the point (-2,-6) and plug it in:
-6=(-3/7)(-2)+b
-6=6/7+b
-6-6/7=b
-48/7=b
Now finish writing the equation:
y=(-3/7)x-48/7
I hope this helps!
-HuronGirl
