Final answer:
To find the equation of line k, which is perpendicular to line j with a slope of 3 and passes through (9, -5), we calculate the slope of line k as -1/3 and use the point to determine the y-intercept, resulting in the equation y = (-1/3)x - 2.
Step-by-step explanation:
The equation provided for line j appears to be a typo, but based on the context provided, we can deduce that its slope (m term) is 3. For a line k to be perpendicular to line j, its slope must be the negative reciprocal of line j's slope. Thus, the slope of line k is -1/3.
To find the equation of line k in slope-intercept form (y = mx + b), we use the point it passes through, which is (9, –5). We substitute the slope and this point into the slope-intercept form to find the y-intercept (b):
y = (-1/3)x + b
-5 = (-1/3)(9) + b
b = -5 + 3
b = -2
Thus, the equation of line k is y = (-1/3)x - 2.