On a coordinate plane, 2 lines are shown. Line H J has points (negative 4, negative 2) and (0, 4). Line F G has points (negative 4, 1) and (0, negative 2). Which statement best explains the relationship between lines FG and HJ? They are perpendicular because their slopes are equal. They are perpendicular because their slopes are negative reciprocals. They are not perpendicular because their slopes are equal. They are not perpendicular because their slopes are not negative reciprocals.

The slope of HJ (3/2) and the slope of FG (-3/4) are not negative reciprocal, so, they are not perpendicular. (Option D).

Recall:

Given that lines HJ (blue line) and FG (red line) are on a coordinate plane as shown in the diagram attached below, let's find their slope:

Slope of line HJ:

Slope of line FG:

Therefore, the slope of HJ (3/2) and the slope of FG (-3/4) are not negative reciprocal, so, they are not perpendicular. (Option D).

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They are not perpendicular because their slopes are not negative reciprocals.

Step-by-step explanation:

Well first we need to find slope.

Line HJ)

(-4,-2) , (0,4)

y2 is 4 y1 is -2, so 4 - -2 = 6

0 - -4 = 4

6/4 -> 3/2

Due to the point (0,4) having no x value 4 is the y intercept.

Hence, y = 3/2x + 4 is the slope of line HJ

Line FG)

(-4,1) , (0,-2)

y2 is -2 y1 is 1, so -2 - 1 = -3

0- -4 = 4

Because (0,-2) is missing an x value -2 is the y intercept,

Equation: y = -3/4x - 2

They are not perpendicular because their slopes are not negative reciprocals.

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step-by-step explanation: