Final answer:
After rearranging the equation 3x - 4y + 7 = 3y + 1 to the form y = (3/7)x + 6/7, we can see that it satisfies the standard form of a linear equation, confirming that it is indeed linear. The answer is yes.
Step-by-step explanation:
To determine whether 3x - 4y + 7 = 3y + 1 is a linear equation, we can rewrite it in the standard form of a linear equation, which is y = a + bx, where a is the y-intercept and b is the slope. First, we need to combine like terms by getting all the y terms on one side of the equation and the x and constant terms on the other side.
Let's rearrange the equation:
- 3x - 4y - 3y = 1 - 7
- 3x - 7y = -6
- y = (3/7)x + 6/7
The rearranged equation is now in the form of y = a + bx, with a = 6/7 and b = 3/7. Since there are no powers of x higher than 1 and y is by itself on one side, this confirms that the equation is indeed linear. The answer is yes, the equation is linear.