Find k so that the line through (5,4) and (k,7) is a) parellel to 5y-2x=6 b) perpendicular 2y+3x=7

Recall that the slopes of two parallel lines are identical, and that the slopes of two perpendicular lines are the negative reciprocal of each other.we only need one of these pieces of information and only one of the equations, a or b.let's pick a and solve to find its slope-intercept form  so that we have its slope. this slope will be the same as the desired line.so our slope is  .now, we have two points which the line must pass through, but the x-coordinate of one of these points is a variable. nevertheless, we know what the slope must equal, so we can solve for the slope given these two points and set it equal to two-fifths.we solve this by cross-multiplying.and that is our final answer.edit: it's impossible to have a line that is parallel to the first one, which has a slope of 2/5, and perpendicular to the second line, which has a slope of -3/2. are you sure you typed this correctly?