Question

The line I is perpendicular to the line y = (3/5)x + (11/5). The point (-6,1) is on the line I. Which of the following is an equation for line I?

A. y = (-5/3)x - 27
B. y = (-5/3)x + 33
C. y = (3/5)x + 13
D. y = (3/5)x - 33

Answer 1

The equation for the line perpendicular to y = (3/5)x + (11/5) and passing through the point (-6,1) is y = (-5/3)x + 11.

Step-by-step explanation:

To find the equation of the line perpendicular to y = (3/5)x + (11/5) and passing through the point (-6,1), we need to determine the slope of the perpendicular line. The slope of the given line is 3/5, so the slope of the perpendicular line will be the negative reciprocal of 3/5, which is -5/3. Using the point-slope form of a line, we can write the equation as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Substituting the values (x1, y1) = (-6,1) and m = -5/3, the equation becomes y - 1 = (-5/3)(x - (-6)). Simplifying, we get y = (-5/3)x + 33/3, which simplifies to y = (-5/3)x + 11. Therefore, the equation for the line perpendicular to y = (3/5)x + (11/5) is y = (-5/3)x + 11.