Question

How do I determine whether 3x-4y+7=3y is a linear equation and how do I write it in standard form?? (I learned this already but for some reason my mind is blank) I’m studying for my final and I’m stressing out please help!!

Answer 1

Equation of the straight line can be given in more form. The most common forms are implicit (general or standard) form ax+by+c=0 and explicit form y=kx+i, where k is line coefficient and l is cut which line made on the y axis. If k>0 then the angle that takes straight line  with the positive direction to the x axis is sharp and if k<0 then the angle that takes straight line with positive direction to the x axis is obtuse. In you case  you only need to form one monomial with variable y in the given equation in the following way: 3x-4y+7=3y => add to both side (-3y) and you get 3x-4y-3y+7=3y-3y finally we get implicit or general 3x-7y+7=0. If is it necessary to transform from the implicit into the explicit form we will do this in the following way: 3x-7y+7=0 add to both side expression (-3x-7) => 3x-3x-7y+7-7=-3x-7 => divide both side with (-7) => y= (-3x-7)/ (-7) => finally we get y=3/7 x + 1 ( in our case coefficient of direction k=3/7 and the cut which line is made3 on the y axis l=1). Its display in the decartes coordinate system is given in one of the already given answers.