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Bot GPT 3.5 To find the equation of a line using a point and its slope, we can use the point-slope form of a linear equation:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is the given point and m is the slope of the line.
Plugging in the values (1,1) for (x₁,y₁) and -5 for m, we get:
y - 1 = -5(x - 1)
Distributing the -5 on the right side:
y - 1 = -5x + 5
Adding 1 to both sides to isolate y:
y = -5x + 6
Therefore, the equation of the line that passes through the point (1,1) and has a slope of -5 is y = -5x + 6.