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Determine the intercepts of the line.

Do not round your answers.
\[ y=-3x+12\]
\[y\]-intercept:
\[\Big(\]

\[,\]
\[\Big)\]
\[x\]-intercept:
\[\Big(\]

\[,\]
\[\Big)\]

1 answer

To determine the intercepts of the line given by the equation \( y = -3x + 12 \), we need to find both the \( y \)-intercept and the \( x \)-intercept.

\( y \)-intercept

The \( y \)-intercept occurs when \( x = 0 \). We can substitute \( x = 0 \) into the equation:

\[ y = -3(0) + 12 = 12 \]

Thus, the \( y \)-intercept is: \[ \Big( 0, 12 \Big) \]

\( x \)-intercept

The \( x \)-intercept occurs when \( y = 0 \). We can set \( y = 0 \) in the equation:

\[ 0 = -3x + 12 \]

To solve for \( x \), we rearrange the equation:

\[ 3x = 12 \] \[ x = \frac{12}{3} = 4 \]

Thus, the \( x \)-intercept is: \[ \Big( 4, 0 \Big) \]

Summary of Intercepts

  • \( y \)-intercept: \( \Big( 0, 12 \Big) \)
  • \( x \)-intercept: \( \Big( 4, 0 \Big) \)