18. Which graph shows the line represented by the equation \( 3 x-4 y=12 \) ?

To determine which graph represents the equation \( 3x - 4y = 12 \), let's analyze and transform the equation into the **slope-intercept form** \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. ### Step 1: Solve for \( y \) Starting with the given equation: \[ 3x - 4y = 12 \] Subtract \( 3x \) from both sides: \[ -4y = -3x + 12 \] Divide every term by **-4** to solve for \( y \): \[ y = \frac{3}{4}x - 3 \] ### Step 2: Identify Key Features From the slope-intercept form \( y = \frac{3}{4}x - 3 \): - **Slope (\( m \))**: \( \frac{3}{4} \) - This means the line rises 3 units for every 4 units it moves to the right. - **Y-intercept (\( b \))**: \( -3 \) - The line crosses the y-axis at the point \( (0, -3) \). ### Step 3: Determine the X-intercept To find where the line crosses the x-axis, set \( y = 0 \) and solve for \( x \): \[ 0 = \frac{3}{4}x - 3 \] \[ \frac{3}{4}x = 3 \] \[ x = 4 \] - **X-intercept**: \( (4, 0) \) ### Step 4: Sketching the Graph With the intercepts and slope identified: 1. **Plot the Y-intercept** at \( (0, -3) \). 2. **Plot the X-intercept** at \( (4, 0) \). 3. **Draw the line** passing through these two points. 4. **Ensure the slope** reflects a rise of 3 units for every run of 4 units to the right. ### Summary The graph of the equation \( 3x - 4y = 12 \) is a straight line that: - **Slopes upward** from left to right with a slope of \( \frac{3}{4} \). - **Intercepts the y-axis** at \( (0, -3) \). - **Intercepts the x-axis** at \( (4, 0) \). When presented with multiple graph options, look for the line that matches these characteristics.