xplain how to find \( x \) - and \( y \)-intercepts.

To find the \( x \)- and \( y \)-intercepts of a function or equation, you can follow these steps: ### Finding the \( x \)-intercept: 1. **Set \( y = 0 \)**: To find the \( x \)-intercept, you need to determine where the graph of the equation crosses the \( x \)-axis. At this point, the value of \( y \) is zero. 2. **Solve for \( x \)**: Substitute \( y = 0 \) into the equation and solve for \( x \). The solution(s) you find will give you the \( x \)-intercept(s). 3. **Write the intercept as a point**: The \( x \)-intercept can be expressed as a point in the form \( (x, 0) \). ### Example: For the equation \( y = 2x + 4 \): - Set \( y = 0 \): \( 0 = 2x + 4 \) - Solve for \( x \): \( 2x = -4 \) → \( x = -2 \) - The \( x \)-intercept is \( (-2, 0) \). ### Finding the \( y \)-intercept: 1. **Set \( x = 0 \)**: To find the \( y \)-intercept, you need to determine where the graph of the equation crosses the \( y \)-axis. At this point, the value of \( x \) is zero. 2. **Solve for \( y \)**: Substitute \( x = 0 \) into the equation and solve for \( y \). The solution you find will give you the \( y \)-intercept. 3. **Write the intercept as a point**: The \( y \)-intercept can be expressed as a point in the form \( (0, y) \). ### Example: For the same equation \( y = 2x + 4 \): - Set \( x = 0 \): \( y = 2(0) + 4 \) - Solve for \( y \): \( y = 4 \) - The \( y \)-intercept is \( (0, 4) \). ### Summary: - The \( x \)-intercept is found by setting \( y = 0 \) and solving for \( x \). - The \( y \)-intercept is found by setting \( x = 0 \) and solving for \( y \). - The intercepts can be expressed as points: \( (x, 0) \) for the \( x \)-intercept and \( (0, y) \) for the \( y \)-intercept.