Question

What is the equation for line s, which is perpendicular to line r (y = x - 6) and includes the point (9, 1)?

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

Answer 1

The equation for line s, which is perpendicular to line r (y = x - 6) and includes the point (9, 1), is y = -x + 10.

Step-by-step explanation:

The equation for line s, which is perpendicular to line r (y = x - 6) and includes the point (9, 1), can be found using the concept of perpendicular lines. The slope of line r is 1, so the slope of line s will be the negative reciprocal of 1, which is -1. Using the point-slope form of a line, we can plug in the slope (-1) and the coordinates (9, 1) into the equation y - y1 = m(x - x1), where (x1, y1) is the point on the line. By substituting the values, we get y - 1 = -1(x - 9). Simplifying the equation, we get y - 1 = -x + 9. Rearranging the equation, we get y = -x + 10. Therefore, the equation for line s is y = -x + 10.

To find a line perpendicular to another line, you need to consider the negative reciprocal of the slope of the given line.