Question

What is the equation, in point-slope form, for a line that goes through (2,-6) and has a slope of -3/4?

A) y + 6 = -(3/4)(x - 2)
B) y - 6 = -(3/4)(x + 2)
C) y - 6 = (3/4)(x - 2)
D) y + 6 = (3/4)(x + 2)

Answer 1

The point-slope form of a line passing through the point (2,-6) with a slope of -3/4 is y + 6 = -(3/4)(x - 2), which is option A.

Step-by-step explanation:

The equation of a line in point-slope form that goes through the point (2,-6) with a slope of -3/4 is given by:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line and m is the slope. Plugging in the given point and slope, we get:

y - (-6) = (-3/4)(x - 2)

Which simplifies to:

y + 6 = -(3/4)(x - 2)

Therefore, the correct option is:

A) y + 6 = -(3/4)(x - 2)