\( 1<\quad \) Use intercepts to graph the equation. \[ 3 x-5 y-15=0 \]

To graph the equation \( 3x - 5y - 15 = 0 \) using intercepts, we will find both the x-intercept and the y-intercept. ### Step 1: Find the x-intercept The x-intercept occurs when \( y = 0 \). We can find it by substituting \( y = 0 \) into the equation: \[ 3x - 5(0) - 15 = 0 \] This simplifies to: \[ 3x - 15 = 0 \] Now, solving for \( x \): \[ 3x = 15 \\ x = 5 \] So, the x-intercept is \( (5, 0) \). ### Step 2: Find the y-intercept The y-intercept occurs when \( x = 0 \). We can find it by substituting \( x = 0 \) into the equation: \[ 3(0) - 5y - 15 = 0 \] This simplifies to: \[ -5y - 15 = 0 \] Now, solving for \( y \): \[ -5y = 15 \\ y = -3 \] So, the y-intercept is \( (0, -3) \). ### Step 3: Plot the intercepts Now that we have both intercepts, we can plot the points \( (5, 0) \) and \( (0, -3) \) on a coordinate plane. ### Step 4: Draw the line Finally, we can draw a straight line through these two points to represent the equation \( 3x - 5y - 15 = 0 \). ### Summary of intercepts: - x-intercept: \( (5, 0) \) - y-intercept: \( (0, -3) \) This completes the process of using intercepts to graph the equation.