Find the \( x \) - and \( y \)-intercepts for the following equation. Then use the intercepts to graph the equation. \( y=2 x+5 \) \( x \)-intercept: \( y \)-intercept: \( (0 \),

1. **Find the \( y \)-intercept:** The \( y \)-intercept occurs when \( x=0 \). Substitute \( x=0 \) into the equation: \[ y = 2(0) + 5 = 5. \] So, the \( y \)-intercept is \( (0,5) \). 2. **Find the \( x \)-intercept:** The \( x \)-intercept occurs when \( y=0 \). Set \( y=0 \) in the equation and solve for \( x \): \[ 0 = 2x + 5. \] Subtract \( 5 \) from both sides: \[ -5 = 2x. \] Divide both sides by \( 2 \): \[ x = -\frac{5}{2}. \] So, the \( x \)-intercept is \( \left(-\frac{5}{2}, 0\right) \). 3. **Graphing the Equation:** - Plot the \( y \)-intercept \( (0,5) \). - Plot the \( x \)-intercept \( \left(-\frac{5}{2}, 0\right) \). - Draw a straight line through these two points. The line extends infinitely in both directions. The intercepts are: - \( x \)-intercept: \( \left(-\frac{5}{2}, 0\right) \) - \( y \)-intercept: \( (0,5) \)