Question

What is the equation of the line that is perpendicular to the given line and passes through the point (3, 4)?

a) y = x + 5
b) y = -x + 3
c) y = 3x + 2
d) y = 3x - 5

Answer 1

To find the equation of a line that is perpendicular to a given line, determine the negative reciprocal of the slope and use the point-slope form of a linear equation. The equation of the line that is perpendicular to the given line with a slope of 3 and passes through the point (3, 4) is y = -x + 3.

Step-by-step explanation:

To find the equation of a line that is perpendicular to a given line, you need to determine the negative reciprocal of the slope of the given line and use the point-slope form of a linear equation.

The given line has a slope of 3, so the perpendicular line will have a slope of -1/3 (negative reciprocal). Using the point-slope form with the point (3, 4), the equation of the perpendicular line is y = -1/3(x - 3) + 4, which simplifies to y = -1/3x + 5.

Therefore, the correct answer is Option B) y = -x + 3.