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There are several questions here. I will answer the first one and ask you to post the rest separately or solve them using the technique used in the first one.
Write an equation in slope-intercept form of a line with the following characteristics:parallel to the graph of:x+y=6 and passes through (1,-4)
The slope-intercept form is: y = mx + b m is the slope, b is the intercept
The graph of x+y=6 has slope -1
because y changes by -1 if x changes by 1
or it is tilted like this: \
and the equation is: y = -1x + 6 slope is -1
Your equation is y=-1x + b because m is -1
Parallel lines have the same slope.
The point (1,-4) is on the line
Plug in x=1, y = -4 and find b
-4 = -1*1 + b
-4 = -1 + b
-3 = b
b= -3
m=-1 and b=-3
y = -x -3
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