Given the following:
(-6, 4) and (2, 0) are the lines that passes through the point.
we are asked to choose the point slope equation.
before we can solve it, we must first of all solve for the slope.
Slope m = y2 - y1
x2 - x1
where:
x1 = -6
x2 = 2
y1 = 4
y2 = 0
m = 0 - 4
2 - (-6)
m = -4/8
m = -1/2
The equation of the lines is found using the point-slope form:
y - y1 = m(x - x1)
so lets substitute into the above equation:
recall, y1 = 4, x1 = -6, slope m = -1/2
y - 4 = -1/2(x - (-6))
y - 4 = -1/2(x + 6)
Therefore, the equation of the lines using the point-slope form is:
y - 4 = -1/2(x + 6)
so the correct option is D which is y - 4 = -1/2(x + 6)
