Final answer:
The equation of line k, which is perpendicular to line j and passes through (8, – 4), is y = −1/6x – 10/3.
Step-by-step explanation:
To find the equation of line k which is perpendicular to line j with equation y+6=6(x–1), we first need to determine the slope of line j. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Rearranging the equation of line j into this form gives us y = 6x - 12, which means the slope of line j is 6.
Since line k is perpendicular to line j, its slope will be the negative reciprocal of 6, which is −6−1 or −1/6. Now we know the slope of line k, we can use the point-slope form to find its equation, with the point given as (8, – 4). The point-slope form is y – y1 = m(x – x1), where (x1, y1) is a point on the line.
Using (8, – 4) and the slope −1/6, the equation of line k will be y – (– 4) = −1/6(x – 8) which simplifies to y + 4 = −1/6x + 4/3. Reformatting into slope-intercept form, the equation of line k becomes y = −1/6x + 4/3 – 4 or y = −1/6x – 10/3.