rewrite the equation 2x-3y= -6 as a function of x.
My answer.
f (x) = (2)/(3) x + 2
No.
2x=3y - 6
divide by two.
x=3/2 y -2
hold on i was looking it over. wouldn't it be:
2x-3y=-6
would actually be:
-3y=-2x-6
y= 2/3x+2
because you said that it would be x=3/2y-2
but how can that be?
You're correct, my previous response had an error. Let's go through the steps to rewrite the equation 2x - 3y = -6 as a function of x correctly.
Starting with the equation 2x - 3y = -6, we want to isolate x on one side of the equation.
Step 1: Move the term with y to the other side:
2x = 3y - 6
Step 2: Divide both sides by 2 to isolate x:
x = (3y - 6)/2
So the correct equation, as a function of x, is:
f(x) = (3y - 6)/2
However, we need to substitute y in terms of x to simplify the equation further.
To do that, we need to solve the equation for y:
2x - 3y = -6
Step 1: Move the term with x to the other side:
-3y = -2x - 6
Step 2: Divide both sides by -3 to isolate y:
y = (2x + 6)/3
Now substitute this in the equation f(x) = (3y - 6)/2:
f(x) = (3(2x + 6)/3 - 6)/2
= (2x + 6 - 6)/2
= (2x)/2
= x
So the correct equation, as a function of x, is:
f(x) = x