Question Find the \( x \)-intercept of the following line. \[ y=\frac{8}{7} x+4 \]

To find the \( x \)-intercept of the line given by the equation: \[ y = \frac{8}{7}x + 4 \] **Step 1: Understand the \( x \)-Intercept** The \( x \)-intercept is the point where the line crosses the \( x \)-axis. At this point, the value of \( y \) is **0**. **Step 2: Set \( y = 0 \) and Solve for \( x \)** \[ 0 = \frac{8}{7}x + 4 \] Subtract 4 from both sides: \[ -\frac{8}{7}x = 4 \] **Step 3: Isolate \( x \)** Multiply both sides by \( \frac{7}{8} \) to solve for \( x \): \[ x = 4 \times \left( -\frac{7}{8} \right) \] \[ x = -\frac{28}{8} \] Simplify the fraction: \[ x = -\frac{7}{2} \quad \text{or} \quad -3.5 \] **Step 4: Write the \( x \)-Intercept as a Point** The \( x \)-intercept is the point where \( y = 0 \), so: \[ \left( -\frac{7}{2},\ 0 \right) \quad \text{or} \quad (-3.5,\ 0) \] **Final Answer:** The \( x \)-intercept of the line \( y = \frac{8}{7}x + 4 \) is \( \boxed{\left( -\frac{7}{2},\ 0 \right)} \).