Graph the equation. \( x-3 y=5 \)

Rewrite the equation by following steps: - step0: Rewrite in slope-intercept form: \(x-3y=5\) - step1: Move the expression to the right side: \(-3y=5-x\) - step2: Divide both sides: \(y=-\frac{5}{3}+\frac{1}{3}x\) - step3: Rearrange the terms: \(y=\frac{1}{3}x-\frac{5}{3}\) To graph the equation \( x - 3y = 5 \), we first convert it into slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. 1. Start with the original equation: \[ x - 3y = 5 \] 2. Rearranging it to solve for \( y \): \[ -3y = -x + 5 \] \[ y = \frac{1}{3}x - \frac{5}{3} \] Now, we have the equation in slope-intercept form: \[ y = \frac{1}{3}x - \frac{5}{3} \] ### Key Features: - **Slope (m)**: \( \frac{1}{3} \) (indicating that for every 3 units you move right, you move 1 unit up) - **Y-intercept (b)**: \( -\frac{5}{3} \) (the point where the line crosses the y-axis) ### Graphing Steps: 1. Start at the y-intercept \( (0, -\frac{5}{3}) \). 2. From this point, use the slope to find another point. Move 3 units to the right (to \( x = 3 \)) and 1 unit up (to \( y = -\frac{5}{3} + 1 = -\frac{2}{3} \)), giving you the point \( (3, -\frac{2}{3}) \). 3. Draw a line through these points to represent the equation. This line represents the equation \( x - 3y = 5 \).