Which best describes the relationship between the line that passes through the points (-9, 2) and (-5, 4) and the line that passes through the points (-3, 4) and (1,6)?

A)parallel
B) same line
C) neither perpendicular nor parallel
D) perpendicular

The lines are parallel to each other.

To figure this out you need to use the formula: m = y2 - y1 / x2 - x1

m represents the slope of the line.

So for the first line:

m = 4 - 2 ÷ -5 - (-9)

m = 2 / 4

Simplify: m = 1 / 2

The slope of the first line is 1 / 2.

For the second line:

m = 6 - 4 ÷ 1 - (-3)

m = 2 / 4

Simplify: m = 1 / 2

So, you can see that the slopes of both lines are the same. When the slopes are the same, that means that the lines are parallel to each other. When the coordinates are the same, that means that the lines are the same. When the slopes are flipped to each other and have are the opposite sign (positive or negative), then the lines are perpendicular.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

step-by-step explanation:

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