Consider the graph of the line y = x – 4 and the point (−4, 2). the slope of a line parallel to the given line is . a point on the line parallel to the given line, passing through (−4, 2), is . the slope of a line perpendicular to the given line is . a point on the line perpendicular to the given line, passing through (−4, 2), is .

The graph represents all the lines and points. Refer calculations for all the answers.

Step-by-step explanation:

The given line is . The point is .

The given line, in slope intercept form, can be written as

Now, the slope of the given line is 1.

So, the slope of the line parallel to the given line will be equal which is 1.

The line parallel to the given line and passing through the point will be,

So, the point on the above line will be,

The point will be .

Slope of the line perpendicular to the given line will be,

Equation of line perpendicular to the given line and passing through   will be,

Now, the point on the above line will be,

The point will be .

Refer the graph.

For more details, refer the link:

link

We have that
Consider the graph of the line y = x – 4 and the point (−4, 2). 

part 1)The slope of a line parallel to the given line is

the slope m of the given line
y=x-4-----> y=(1)*x-4
is m=1

the answer Part 1) is
m=1

Part 2) A point on the line parallel to the given line, passing through (−4, 2)

the slope m=1
y-y1=m*(x-x1)------> y-2=(1)*(x+4)-----> y=x+4+2------> y=x+6

the answer Part 2) is
y=x+6

part 3) The slope of a line perpendicular to the given line is .

we know that 
when two lines are perpendicular
m1*m2=-1
m1=1
m2=-1

the answer part 3) is
m=-1

Part 4) A point on the line perpendicular to the given line, passing through (−4, 2), is 
the slope m=-1
y-y1=m*(x-x1)------> y-2=(-1)*(x+4)-----> y=-x-4+2------> y=-x-2

the answer Part 4) is
y=-x-2

see the attached figure

What are the options

We need more info then that