How do I solve for y, so that i can graph it?

y - x/9 = 2

Is it solved for y? No.

We have to do something about that x/9.

What is x/9 doing?
It is subtracting (from y).

What is the opposite of subtracting?

So we add x/9 to both sides:

y = 2 + x/9

Is it solved for y? Yes.

Does it look like y = mx + b?

Not exactly.

Then let's arrange it a little:

y = x/9 + 2

y = (1/9)x + 2

Ta da!
9y-x=18

Before you divide, isolate the y variable. Add x to both sides

9y=x+18

Divide both sides by 9. That means all terms, 9y/9, x/9 or 1/9*x, and 18/9.

Simplify:
y=1/9x+2

You now have everything to graph the line in slope intercept form: y=mx+b. The y intercept is 2, and the slope is 1/9.

Whether you divide all terms by 9 first and get:

y-x/9=2

Or whether you add x to both sides and get:

9y=18+x

You need to identify the terms and ask yourself what they want solved. They want the equation solved for y which means the y variable by itself equals everything else.

If you have y-x/9=2, what is stopping y from being by itself? -x/9. To get rid of it, add the inverse to both sides and get y=1/9x+2.

If you have 9y=18+x, what is stopping y from being by itself? 9y. To get rid of it, multiply the inverse to both sides and get the same thing.
change the line into the intercept form : x/a + y/b = 1

where 'a' is x intercept and 'b' is y intercept now plot the points (a,0) and (0,b) on the graph and draw a line passing through the plotted graph.

Boom you got the graph
If I'm reading the comments correctly, I was doing okay the second time around by ADDING X to both sides, and messed up by not converting x/9 into 1/9x?
You don’t need to eliminate x or y. The equation is for a linear graph, so once you’re able to find 2 different points on the graph, you’re good to go.

The simplest solution:

1. Isolate the y:

9y - x = 18

9y = x + 18

y = (x + 18)/9

y = (1/9)x + 2 -> this is the equation for a line in the form of y = mx + c; the x and y values are variable, the m value is the gradient (the rate by which y increases in relation to x), and the c is the y-intercept - or the number you have with 0x.

2. Obtain 2 points on the graph

All that’s left to do is plug 2 random real numbers for x values (i like to use 0, then a random integer). Then plot the resulting two points (x value you chose, resulting y value) then connect the dots.

For your case, notice that the gradient/slope is 1/9? That means that with each +1 increase in x, y increases by 1/9. For example, if you increase the x value by 4 at any given point, the resulting y value increases by 4*(1/9)=4/9

So if you want to avoid fractions (like most normal people would), you should plug multiples of 9 in x, because increasing by 1/9 9 times overall is an increase of 9/9 = 1.

This would make graphing easier.

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