1. these four lines have been graphed on the same coordinate grid. which lines are parallel to each other?
line j: y=1/4x+4
line k: y=1/4x+3
line l: y=3x+4
line m: y=4x+1/4

a. j and k
b. j and m
c. l and k
d. l and m

2. find the equation of a line perpendicular to y-3x=-8 that passes through the point (3, 2).
a. y=-3x+2
b. y=-3x+3
c. y=-1/3x+2
d. y=-1/3x+3

3. find the point, m, that divide segment segment ab into a ratio of 5: 2 if a is at (1, 2) and b is at (8, 16).
a. (6, 12)
b. (-6, 12)
c. (6, -12)
d. (-6, -12)

4. find the distance between (4, 2) and (-4, -4).
a. 2
b. square root of 10
c. 4
d. 10

1)a. j and k

2) d.

3)a. (6, 12)

4)d. 10

Step-by-step explanation:

1) Lines are said to parallel if their slopes are same.

General form of line =  --1

where m is the slope

On comparing all lines with 1

So, Slope of line j =

Slope of line k =

Slope of line l = 3

Slope of line m = 4

Slope of line j and k are same

So, Option a is correct.

a. j and k

2) Find the equation of a line perpendicular to y-3x=-8 that passes through the point (3, 2).

y=-8+3x

On comparing with 1

Slope of given line is 3

Now slope of a line which is perpendicular to the given line

Two lines are said to be perpendicular if the product of their slopes is -1

So,

So, slope of perpendicular line is  

General form of line =  -1

Substitute m = and passing points (3,2)

So, Now substitute value of m and c in 1

Hence the equation of a line perpendicular to y-3x=-8 that passes through the point (3, 2) is

Option d is correct.

3) Find the point, M, that divide segment segment AB into a ratio of 5:2 if A is at (1, 2) and B is at (8, 16).

m:n=5:2

To find coordinates of M we will sue section formula:

and

    and

    and

Thus the coordinates of M is (6,12)

Hence Option A is correct.

4). Find the distance between (4, 2) and (-4, -4).

Substitute the values in the formula :

Thus the distance is 10

Hence Option D is correct.

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