Graphing a line by first finding its \( x \)-and \( y \)-intercepts The equation of a line is given below. \[ 5 x+4 y=10 \] Find the \( x \)-intercept and the \( y \)-intercept. Then use them to graph the line. \( x x \)-intercept: \( y \)-intercept:

**Step 1: Find the \( x \)-intercept** Set \( y=0 \) in the equation: \[ 5x + 4(0) = 10 \] This simplifies to: \[ 5x = 10 \quad \Longrightarrow \quad x = \frac{10}{5} = 2 \] Thus, the \( x \)-intercept is at \((2, 0)\). **Step 2: Find the \( y \)-intercept** Set \( x=0 \) in the equation: \[ 5(0) + 4y = 10 \] This simplifies to: \[ 4y = 10 \quad \Longrightarrow \quad y = \frac{10}{4} = \frac{5}{2} \] Thus, the \( y \)-intercept is at \(\left(0, \frac{5}{2}\right)\). **Step 3: Graph the Line** Plot the points \((2, 0)\) and \(\left(0, \frac{5}{2}\right)\) on a coordinate plane. Draw a straight line through these two intercepts to graph the line defined by the equation \(5x + 4y = 10\).