4) The equation of line p is 5x-3y=18 Line q, which is perpendicular to line D. indudes the point (-6,2) . What is the equation of line q?

To find the equation of line q, we first need to find the slope of line p. We can do this by rearranging the equation of line p in slope-intercept form (y = mx + b), where m is the slope.<br /><br />The equation of line p is 5x - 3y = 18. Rearranging this gives us y = (5/3)x - 6. Therefore, the slope of line p is 5/3.<br /><br />Since line q is perpendicular to line p, the slope of line q is the negative reciprocal of the slope of line p. Therefore, the slope of line q is -3/5.<br /><br />We know that line q passes through the point (-6, 2). We can use the point-slope form of a line (y - y1 = m(x - x1)) to find the equation of line q. Substituting the given point and slope into this equation gives us y - 2 = -3/5(x + 6).<br /><br />Simplifying this equation gives us y = -3/5x - 12/5 + 2 = -3/5x - 12/5 + 10/5 = -3/5x - 2/5. Therefore, the equation of line q is y = -3/5x - 2/5.