To graph the equation \( y = -12x - 6 \), we can follow these steps:
-
Identify the slope and y-intercept: The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Here, \( m = -12 \) and \( b = -6 \).
- Slope (\( m \)): -12 (This means for every 1 unit increase in \( x \), \( y \) will decrease by 12 units).
- Y-intercept (\( b \)): -6 (This is where the line crosses the y-axis).
-
Plot the y-intercept: Start by plotting the point (0, -6) on the y-axis.
-
Use the slope to find another point: From (0, -6), use the slope to determine another point:
- Since the slope is -12, you can move 1 unit to the right (increase \( x \) by 1) and then move 12 units down (decrease \( y \) by 12).
- From (0, -6), move to (1, -18).
-
Plot the second point: Plot the point (1, -18) on the graph.
-
Draw the line: Draw a straight line through the points (0, -6) and (1, -18), continuing in both directions.
-
Add a few more points (optional): You can check your graph by plugging in a few values of \( x \) to find corresponding \( y \) values:
- If \( x = -1 \): \[ y = -12(-1) - 6 = 12 - 6 = 6 \] So plot the point (-1, 6).
- If \( x = 2 \): \[ y = -12(2) - 6 = -24 - 6 = -30 \] So plot the point (2, -30).
After plotting these points and drawing the line, you will have the graph of the equation \( y = -12x - 6 \). The line will have a steep negative slope, moving down sharply from left to right.