Question

What is the equation of the line perpendicular to the line y = -x + 2 and passes through the point (3, 5)?

A) y = x + 2
B) y = x - 2
C) y = -x + 8
D) y = -x + 11

Answer 1

The equation of the line perpendicular to y = -x + 2 and passes through the point (3, 5) is y = x + 2.

Step-by-step explanation:

To find the equation of a line perpendicular to y = -x + 2 and passing through the point (3, 5), we need to determine the slope of the given line and then find the negative reciprocal of that slope. The given line has a slope of -1. The negative reciprocal of -1 is 1, so the slope of the perpendicular line is 1.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), we can substitute the values of (x1, y1) = (3, 5) and m = 1 into the equation. This gives us y - 5 = 1(x - 3), which simplifies to y - 5 = x - 3. Finally, rearranging the equation, we get y = x + 2.

Therefore, the equation of the line perpendicular to y = -x + 2 and passes through the point (3, 5) is y = x + 2.