Which equation is not an equation of a line?
\[
2 x-3 y=0
\]
\[
\frac{x}{2}-\frac{y}{3}=1
\]
\[
y=x^{2}
\]
\[
y+3(x-2)=0
\]

Answer

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Answer

\(\boxed{y = x^{2}}\) is the equation that is not an equation of a line.

Steps

Step 1 ：Check each equation to see if it can be written in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Step 2 ：Equation 1: \(2x - 3y = 0\) can be written as \(y = \frac{2}{3}x\)

Step 3 ：Equation 2: \(\frac{x}{2} - \frac{y}{3} = 1\) can be written as \(y = \frac{3}{2}x - 3\)

Step 4 ：Equation 3: \(y = x^{2}\) cannot be written in the form \(y = mx + b\)

Step 5 ：Equation 4: \(y + 3(x - 2) = 0\) can be written as \(y = -3x + 6\)

Step 6 ：\(\boxed{y = x^{2}}\) is the equation that is not an equation of a line.