Answer: a) y -6 = -1.21068(x +2) b) y -6 - 0.82598(x +2)Step-by-step explanation:The slope of a line is the tangent of the angle it makes with the +x axis. We are given a point on lines j and k, so we can write the equation of the line if we know its slope. The slope of line m can be found from the two given points on that line: slope = (y2 -y1)/(x2 -x1) = (2 -(-1))/(5 -(-3)) = 3/8a)The angle that line k makes with the x-axis is 109° more than the angle made by line m. The slope of line k can be found using the formula for the tangent of the sum of angles: tan(α+β) = (tan(α)+tan(β))/(1 -tan(α)tan(β))For tan(α) = 3/8, and β = 109°, this becomes ... slope of line k = (3/8 +tan(109°))/(1 -3/8·tan(109°)) = (3 +8tan(109°))/(8-3tan(109°)) ≈ -1.21068__The point-slope formula for a line is ... y -k = m(x -h) . . . . . . line with slope m through point (h, k)Point (-2, 6) is given as being on lines k and j, so the equation of line k can be written ... y -6 = -1.21068(x +2) . . . . equation of line k__b)Line j is perpendicular to line k, so its slope will be the opposite reciprocal: slope line j = -1/(-1.21068) ≈ 0.82598Then the point-slope equation of line j is ... y -6 = 0.82598(x +2) . . . . equation of line j_____Additional commentThe figure shown is impossible. The attachment shows line m through the two given points, and line k making an angle of 109° with it, as calculated above. The angle between lines k and n at the point of intersection with the y-axis cannot be 71° as shown in the given diagram. It is closer to 70°.__The given angles (109°, 71°) are supplementary, suggesting that lines m and n are intended to be parallel. In that case, the intersection point with of line n with the y-axis is (0, 3.5) and the line through that point and (2, 6) can have the equation 5x +4y = 14 (line k). Its perpendicular can have equation 4x -5y = -38 (line j). The angles made by these lines are about 108.1° and 71.9°, not the angles shown in the diagram.