Is the linear equation 3x - 2 = y in standard form? Explain.
Standard form : Ax + By = C
y = 3x -2
y -3x = 3x -3x -2
y-3x = -2
or
-3x + y = -2
To determine if the linear equation 3x - 2 = y is in standard form, we need to consider what standard form looks like. The standard form of a linear equation is written as Ax + By = C, where A, B, and C are constants and A and B are not both zero.
In the given equation, we have 3x - 2 = y. To put it in standard form, we want to rearrange the equation so that it matches the form Ax + By = C.
In this case, the equation is already very close to standard form. We can rewrite it as y = 3x - 2 by adding 2 to both sides of the equation.
Now, let's compare this with the standard form. In standard form, we have Ax + By = C. If we rearrange the equation we obtained, we get -3x + y = -2.
Comparing the rewritten equation with the standard form, we see that the coefficients of x and y are -3 and 1, respectively, and C is -2. Thus, we have -3x + y = -2.
Since the given equation 3x - 2 = y can be rewritten as -3x + y = -2, which matches the form Ax + By = C, we can conclude that it is in standard form.