Consider the equation. Which graph shows a line that is perpendicular to the line defined by the given equation? A. In a linear graph line diagram, A line passes through (minus 4, minus 2) and (2, minus 0.5) which intersects the x-axis at 4 units and the y-axis at minus 1 unit. B. In a linear graph line diagram, A line passes through (2, 0.5) and (minus 4, 2) which intersects the x-axis at 4 units and the y-axis at minus 1 unit. C. In a linear graph line diagram, A line passes through (2, 4) and (0.5, minus 2) which intersects the x-axis at 1 unit and the y-axis at minus 4 units. D. In a linear graph line diagram, A line passes through (2, minus 4) and (0.5, 2) which intersects the x-axis at 1 unit and the y-axis at minus 4 units.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The question is incomplete:

The complete question is:

Consider the equation y = 4x - 2 Which graph shows a line that is perpendicular to the line defined by the given equation?

Please refer to the attached picture.

The given line:

y = 4x - 2

The slope of the line m = 4

The slope of the line which is perpendicular to the above line:

M = -1/4 = -0.25

The graph second has a slope of -0.25

[tex]\rm y\ -2\ =\ \dfrac{\left(2-0.5\right)}{-4-2}\left(x+4\right)[/tex]

y - 2 = -0.25x - 1

y = -0.25x + 1

Thus, the graph second represents the line that is perpendicular to the line y = 4x - 2 option (B) is correct.

Learn more about the slope here:

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