Show that the following 2 lines are parallel: l1: 3y=15x+17 l2: 7y+5=35x

Both of these lines are straight lines since they only have x and y to powers of 1; and constants. Straight lines can be defined if two parameters are known, the gradient and the y-intercept. For two lines to be parallel their gradients must be the same; hence to answer this question we must find the gradients of both lines and show they are equal. The easiest way to find the gradient of a straight line is to arrange the equation of the line in the form y=mx+c, and m is the gradient.Starting with l1, to get the desired form we divide both sides of the equation by 3, giving y=5x+(17/3). Hence the gradient is 5.For l2, first we must take away 5 from both sides of the equation to give 7y=35x-5; and then divide both sides by 7 to give y=5x-(5/7). Hence the gradient is 5.Since both lines have a gradient of 5 they are parallel.