Final answer:
To find the equation of the line perpendicular to line j, we need to find the negative reciprocal of the slope of line j. Using the point-slope form of a linear equation, we substitute the given point and slope into the equation to find the equation of line k: y = 1/3x - 2/3.
Step-by-step explanation:
To find the equation of the line perpendicular to line j, we need to find the negative reciprocal of the slope of line j. The equation of line j is y+3=-3(x-2), which can be rewritten as y=-3x+6. The slope of line j is -3. The negative reciprocal of -3 is 1/3.
Since line k is perpendicular to line j and passes through the point (-2,-4), we can use the point-slope form of a linear equation to find the equation of line k. The point-slope form is y-y1 = m(x-x1), where (x1,y1) is a point on the line and m is the slope.
Using the point (-2,-4) and the slope 1/3, we substitute these values into the point-slope form to get the equation of line k: y-(-4) = 1/3(x-(-2)). Simplifying, we get y+4 = 1/3(x+2). Rearranging, the equation of line k is y = 1/3x - 2/3.