Final answer:
To find the equation of line K, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other. The equation of line K in slope-intercept form is y = -3x + 1.
Correct option is a.
Step-by-step explanation:
To find the equation of line K, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other. The slope of line j is 1/3, so the slope of line K will be -3 (negative reciprocal of 1/3).
Now we can use the point-slope form of a linear equation to find the equation of line K. The point-slope form is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope. We are given that line K passes through the point (3, -8).
Substituting these values into the point-slope form, we get:
y - (-8) = -3(x - 3)
Simplifying the equation, we get:
y + 8 = -3x + 9
y = -3x + 1
Therefore, the equation of line K in slope-intercept form is y = -3x + 1.
Correct option is a.