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: \( \Big( 4, 0 \Big) \)
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