Answer:
y = -x - 4
Step-by-step explanation:
Given:
a line with a slope of -1, passing through the point (2,-6)
Point-Slope Form: y - y₁ = m(x - x₁)
where:
(x₁, y₁) is the given point
m is the slope
Substitute the given values into the formula:
⇒ y - y₁ = m(x - x₁)
⇒ y - (-6) = -1(x - 2)
⇒ y + 6 = -1(x - 2) [distribute -1 through the parentheses]
⇒ y + 6 = -x + 2 [subtract 6 from both sides]
⇒ y + 6 - 6 = -x + 2 - 6
⇒ y = -x - 4
Check your work:
⇒ y = -x - 4 [substitute 2 for x, and -6 for y]
⇒ -6 = -2 - 4 [simplify]
⇒ -6 = -6 ✔
Therefore, the equation of the line is: y = -x - 4
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