Question

Which of the following represents the point-slope form of the equation of the line passing through (3,4) and is parallel to y = -x + 3?

A) y - 4 = -x + 3
B) y - 4 = x - 3
C) y - 4 = -x - 3
D) y - 4 = x + 3

Answer 1

The point-slope form of the equation for the line passing through (3,4) and parallel to y = -x + 3 is y - 4 = -x + 3, which corresponds to option A.

Step-by-step explanation:

The point-slope form of the equation of a line is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Since the given line y = -x + 3 has a slope of -1, and the new line is parallel to it, the new line will also have a slope of -1. Using the point (3,4) on the new line, we substitute into the point-slope form to get y - 4 = -1(x - 3), which simplifies to y - 4 = -x + 3.

Thus, the correct point-slope form is option A) y - 4 = -x + 3.