The equation -2y = 5x + 8 represents a line. What are the slopes of lines that are parallel and perpendicular to the given line?
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Lines parallel to the given equation will have a slope of -⁵/2 and lines perpendicular to the given line will have a slope of ⅖.

Step-by-step explanation:

Given the equation of a line, -2y = 5x + 8, first rewrite the equation in the slope-intercept form, before determining the slope of the lines that will be parallel to it, and slope of lines that will be perpendicular to it.

-2y = 5x + 8

Divide both sides by -2

y = 5x/-2 + 8/2

y = -⁵/2x + 4

The slope of the line of this equation is -⁵/2.

Linea that will be parallel to the given equation will have the same slope, while all lines that will be perpendicular to it will be a negative reciprocal of the slope of the equation.

Therefore:

Lines parallel to the given equation will have a slope of -⁵/2 and lines perpendicular to the given line will have a slope of ⅖.