The equation of the line that passes through the points (4, -4) and (-4, -4) is y = -4.
In the question, we are asked to find the equation of the line that passes through the points (4, -4) and (-4, -4).
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be shown as:
m = (y₂ - y₁)/(x₂ - x₁).
Thus, the slope of the line passing through the points (4, -4) and (-4, -4) can be shown as:
m = (-4 - (-4))/(-4 - 4) = 0/(-8) = 0.
The equation of the line passing through the point (x₁, y₁) and having a slope of m, can be shown as:
y - y₁ = m(x - x₁).
Thus, the equation of the line passing through (4, -4) and having a slope of 0, can be shown as:
y - (-4) = 0(x - 4),
or, y + 4 = 0,
or, y = -4.
Thus, the equation of the line that passes through the points (4, -4) and (-4, -4) is y = -4.
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