Find the slope and \( y \)-intercept of the line. Graph the line. \( x+6 y=36 \)

Rewrite the equation by following steps: - step0: Rewrite in slope-intercept form: \(x+6y=36\) - step1: Move the expression to the right side: \(6y=36-x\) - step2: Divide both sides: \(y=6-\frac{1}{6}x\) - step3: Rearrange the terms: \(y=-\frac{1}{6}x+6\) To find the slope and \( y \)-intercept of the line given by the equation \( x + 6y = 36 \), we first convert it to the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. 1. **Convert to Slope-Intercept Form:** Starting with the equation: \[ x + 6y = 36 \] We can isolate \( y \): \[ 6y = -x + 36 \] Dividing by 6: \[ y = -\frac{1}{6}x + 6 \] 2. **Identify the Slope and \( y \)-Intercept:** From the equation \( y = -\frac{1}{6}x + 6 \): - The slope \( m \) is \( -\frac{1}{6} \). - The \( y \)-intercept \( b \) is \( 6 \). 3. **Graph the Line:** While I cannot plot the graph directly, you can graph the line using the slope and \( y \)-intercept: - Start at the point \( (0, 6) \) on the \( y \)-axis. - From there, use the slope \( -\frac{1}{6} \) to find another point. For every 6 units you move to the right (positive \( x \)), move 1 unit down (negative \( y \)). This will give you a straight line that represents the equation \( x + 6y = 36 \).