what is -5x+3y=15 simplified? how do you get the y where it belongs? Confused algebra student!?

Answer 1

just rearrange the equation:
-5x + 3y = 15
move the 5x to the other side:
3y = 15 + 5x
divide by 3 to get y alone:
y = 5 + 5/3x

Answer 2

Unfortunately, your use of the word "simplified" doesn't make sense here. There are three basic forms of a linear equation (that is, an equation that when you pick a value for x and then solve for y, the points all end up in a line--think of it as LINEar). They are:

1) y = mx + b, where m is the slope of the line, and b is the y-intercept. This is called SLOPE-INTERCEPT form.
2) ax + by = c (or ax + by - c = 0), where a and b are constants. This is called STANDARD form (it's the form your equation is in).
3) y - y1 = m(x - x1), where m is the slope (same as in (1)), and (x1, y1) is any point on the line. This is called POINT-SLOPE form.

All three of these forms are equally correct, and equally useful, so your equation, in standard form, is actually fine as it stands. The only problem with standard form is that it doesn't really tell you anything, unlike (1), slope-intercept form (which is just a simple rearrangement of standard form) which tells you, unsurprisingly, the slope and y-intercept of the line you are studying. So, if you rearrange your equation (remember to do the same operation to both sides of the equation):

-5x + 3y = 15
+5x +5x (add 5x to both sides)
-------------------
3y = 5x + 15
/3 /3 (divide both sides by 3)
-------------------
y = (5/3)x + 5

Now it is in slope intercept form, and the part before the x (5/3) is the slope, and the part at the end (+5) is the y-intercept. The y-intercept means that it cross the y-axis (the vertical axis that goes through the origin) at 5 (that is, the point (0,5)--try it--plug in 0 for x and you will get 5 for y), and the slope means that from that point to get to another point you move positive 3 steps in x and positive 5 steps in y (or, equivalently, negative 3 steps in x and negative 5 steps in y). Remember that slope is how much you change in y divided by how much you change in x (some people like to call it RISE over RUN--rise being up and down (y) and run being left and right (x)).

Bottom line, though, if your teacher asks you to simplify that equation, tell him/her that it already is simplified in standard form.

Answer 3

if -5 is negative on one side of the = sign it's positive on the other just move it, then divide everything by 3 to get y by it's self.
y=5/3x + 5