Is the equation x/3=4-2y linear? If so, what is it in its standard form (Ax+By=C)?

Question

I don’t understand and I have a big test tomorrow on linear functions.

Answer 1

x/3=4-2y

Let's work on this equation:

x = 12 - 6y

-6y = x - 12

y = (x/-6) + 2

Now, the equation is in y = mx + b form.

m, the slope, is (-1/6)

b, the y intercept is 2

So, this is a linear equation. It will plot as a line. Let's try a couple of coordinates:

If x = 0, then y = 2

If x = 1, then y = 1 5/6

If x = 2, then y = 1 4/6

So, for change plus one of x, y will change by minus one sixth. This is the hallmark of a linear equation.

Put in std form:

y = (x/-6) + 2

(-1/6)x = y - 2

(-1/6)x - y = - 2

Or,

(1/6)x + y = 2