Question

Convert the equation with a slope of -1/2 and containing the point (2, -2) from slope-intercept form to point-slope form.

A) y+2=−1/2​(x−2)
B) y−2=−1/2​(x+2)
C) y−2=−1/2​(x−2)
D) y+2=−1/2​(x+2)

Answer 1

The equation of a line with a slope of -1/2 and containing the point (2, -2) in point-slope form is y + 2 = -1/2(x - 2), which is option A.

Step-by-step explanation:

To convert a linear equation with a given slope and a point it passes through from slope-intercept form to point-slope form, one can use the point-slope equation y - y₁ = m(x - x₁), where (x₁, y₁) is the point the line passes through and m is the slope of the line.

In this case, the slope is given as -1/2, and the line contains the point (2, -2). Plugging these values into the point-slope equation, we get y - (-2) = (-1/2)(x - 2), which simplifies to y + 2 = -1/2(x - 2). Therefore, the correct conversion of the equation to point-slope form is:

Option A) y + 2 = -1/2(x - 2)

This conversion reflects a straight line with a negative slope, as a negative slope implies that the line is decreasing from left to right.