Write the point-slope form of the equation of the line through the point (4, -4) with a slope of -2.
A. y + 4 = -2(x + 4)
B. y - 4 = -2(x + 4)
C. y + 4 = -2(x - 4)
D. y - 4 = -2(x - 4)
The correct answer is D. y - 4 = -2(x - 4).
The point-slope form of a line is given by the equation:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
In this case, the point is (4, -4) and the slope is -2. Substituting these values into the equation, we have:
y - (-4) = -2(x - 4)
Simplifying, we get:
y + 4 = -2(x - 4)
Therefore, the point-slope form of the equation of the line is y - 4 = -2(x - 4).
To find the point-slope form of the equation of a line, you can use the formula:
y - y₁ = m(x - x₁),
where (x₁, y₁) is a point on the line and m is the slope of the line.
In this case, the given point is (4, -4) and the slope is -2. Plugging these values into the formula, we have:
y - (-4) = -2(x - 4).
Simplifying the equation, we get:
y + 4 = -2(x - 4).
Therefore, the correct answer is option C:
y + 4 = -2(x - 4).
To find the point-slope form of the equation of a line, we use the formula:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line.
In this case, the given point is (4, -4), and the slope is -2.
Now, substitute these values into the formula:
y - (-4) = -2(x - 4)
Simplifying:
y + 4 = -2(x - 4)
So, the correct answer is option C:
y + 4 = -2(x - 4)