Question

The equation of line j is y = (1/3)x + 1. Line K is perpendicular to line j and passes through (3, -8). What is the equation of line K in slope-intercept form? a) y = -3x - 17 b) y = -3x + 17 c) y = 3x - 17 d) y = 3x + 17

Answer 1

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.