7. Graph the line \( 12 x+4 y=36 \)

Rewrite the equation by following steps: - step0: Rewrite in slope-intercept form: \(12x+4y=36\) - step1: Move the expression to the right side: \(4y=36-12x\) - step2: Divide both sides: \(y=9-3x\) - step3: Rearrange the terms: \(y=-3x+9\) To graph the line given by the equation \( 12x + 4y = 36 \), we first convert it to slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. 1. **Convert to Slope-Intercept Form:** - Start with the original equation: \[ 12x + 4y = 36 \] - Solve for \( y \): \[ 4y = -12x + 36 \] \[ y = -3x + 9 \] Here, the slope \( m = -3 \) and the y-intercept \( b = 9 \). 2. **Identify Key Points:** - The y-intercept is the point \( (0, 9) \). - To find another point, we can choose a value for \( x \). For example, if \( x = 1 \): \[ y = -3(1) + 9 = 6 \] So, another point is \( (1, 6) \). 3. **Plot the Points:** - Plot the points \( (0, 9) \) and \( (1, 6) \) on a graph. 4. **Draw the Line:** - Connect the points with a straight line extending in both directions. This line represents the equation \( 12x + 4y = 36 \). If you have graphing software or graph paper, you can plot these points and draw the line accordingly.