Question

Find the equation of the line that passes through the point (1, -7) and is perpendicular to the line y = (1/9)x - 4. Which of the following options is the correct equation for this line?

A) y = -9x + 2
B) y = -9x - 2
C) y = 9x + 2
D) y = 9x - 2

Answer 1

The equation of the line that passes through the point (1, -7) and is perpendicular to the line y = (1/9)x - 4 is y = -9x - 2.

Step-by-step explanation:

To find the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The given line has a slope of 1/9, so the negative reciprocal would be -9. Using the point-slope form of a linear equation, we can substitute the values of the point (1, -7) and the slope -9 into the equation.

The equation of the line that passes through the point (1, -7) and is perpendicular to the line y = (1/9)x - 4 is y = -9x - 2. Therefore, option B is the correct equation for this line.