Question

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

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

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

Answer 1

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