Write an equation for the line that passes through the point (0, 5) with a slope of -2.
A. y = 5x – 2
B. y = -2x
C. y = -2x – 5
D. y = -2x + 5*
correct
To find the equation of a line that passes through a given point with a specified slope, you can use the point-slope form of a linear equation. The point-slope form is:
y - y₁ = m(x - x₁),
where (x₁, y₁) represents the given point on the line, and m is the slope.
In this case, the given point is (0, 5), and the slope is -2. Substituting these values into the point-slope form, we get:
y - 5 = -2(x - 0).
Simplifying the equation further, we have:
y - 5 = -2x.
To obtain the equation in the standard form (ax + by = c), we can modify the equation by moving the -2x term to the other side and rearranging the terms:
2x + y = 5.
This equation can be written as y = -2x + 5, which matches option D. Hence, the correct equation for the line passing through the point (0, 5) with a slope of -2 is y = -2x + 5.