Determine whether y=2x-1 is a linear equation if so write equation in standard form . ?
MATH is the Subject Area.
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To determine whether an equation is linear, we need to check if it satisfies two conditions:
1. Each term in the equation is either a constant or the product of a constant and a single variable.
2. The highest power of the variable in any term is 1.
In the given equation y = 2x - 1, both conditions are satisfied. Each term (2x and -1) consists of a constant (2 and -1) multiplied by a single variable (x). Also, the highest power of the variable in any term is 1.
Therefore, y = 2x - 1 is a linear equation.
To write the equation in standard form, we need to rearrange the terms so that the variables are on one side of the equation and the constant is on the other side.
y = 2x - 1 (given equation)
To move the constant term (-1) to the other side, we add 1 to both sides of the equation:
y + 1 = 2x
Next, we want to rewrite the equation with the variables on the left side and the constant on the right side. To do this, we can swap the sides of the equation:
2x = y + 1
Finally, to put the equation in standard form, we rearrange it so that the coefficients of the variables are integers:
2x - y = 1
Therefore, the equation y = 2x - 1 in standard form is 2x - y = 1.