Agebra Graphing questions?

Question

Im learning how to graph and I was wondering if someone could show me how to solve this and what to do when Im graphing. Im not understanding it very much and the examples are not all that helpfull

Graph using the intercept method: x + 3y = 6

Answer 1

6/3=2 thats your y intercept so put a point at (0,2)
6/1=6 is your x intercept so put a point at (6,0)
connect the dots and thats your graph.

slope is change in y divided by change in x, so...
(2-0)/(0-6) = -1/3

if you want a better line, move 3 right and 1 down from your current intercepts and youll have more dots to connect

Answer 2

The easiest way to do this is as follows:

Solve for y b/c we want to get in the form of y = mx + b where m is the slope and b is the y-intercept:

first subtract x:

3y = 6 - x

now divide by 3:

y = 6/3 - x/3

which is:

y = 2 - x/3 (keep in mind that x/3 can be written the same as (1/3)*x

From this equation, m (the slope) = -(1/3) and b (the y-intercept -- or where the line will intercept the y-axis) = 2

Now, on your graph, put a point at y = 2 - which is b.. now, we must apply the slope:

m = rise/run -- rise is up and down, run is left to right.

we have m = -1/3, so we must go down 1 and over to the right 3 -- and put another point there.. now, connect your points.. this is the line of your graph...

keep in mind you can continue to go down 1 and over 3 from each point to continue the line on and on..

Answer 3

3y = -x + 6
y = -1/3 x +2

slope is -1/3
y-int is (0,2)
x-int is (6,0)