Write the slope intercept form for an equation of the line that passes through the given point and is parallel to the graph of each.
Ok, let's start by writing the given equation in slope-intercept form. We have 3x+y=12. We need to put it in the form y=mx+b.
y=12-3x (subtract 3x from 12)
y=-3x+12 (rearrange to match slope-intercept form)
We're looking for a parallel line, which means that the slope of the line will be the same as the given line -3. The difference between the given line and the new line will be the intercept (b or 12). So what we need to find is an intercept that will allow a line with a slope of -3 to pass through the point (-1,6).
To do that, we'll plug -1 for x and 6 for y into the equation y=-3x+12 and replace 12 with b.
This gives us:
6=-3(-1) + b.
Now we solve for b:
6=3+b (multiply -3 and -1)
3=b (subtract 3 from 6)
Finally, we put everything together:
This is the equation of the line that is parallel to the given line (3x+y=12) and passes through the point (-1,6).