Questions: Graph the line. y = -x - 4

Transcript text: Graph the line. \[ y=-x-4 \]

Solution

Solution Steps

Step 1: Identify the slope and y-intercept

The given equation is in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. For the equation \( y = -x - 4 \):

Slope (\( m \)) = -1
Y-intercept (\( b \)) = -4

Step 2: Plot the y-intercept

Locate the y-intercept on the graph. The y-intercept is the point where the line crosses the y-axis. For \( y = -x - 4 \), the y-intercept is -4. Plot the point (0, -4) on the graph.

Step 3: Use the slope to find another point

The slope of -1 means that for every 1 unit increase in \( x \), \( y \) decreases by 1 unit. Starting from the y-intercept (0, -4), move 1 unit to the right (positive direction on the x-axis) and 1 unit down (negative direction on the y-axis). This gives the point (1, -5). Plot this point on the graph.

Step 4: Draw the line

Draw a straight line through the points (0, -4) and (1, -5). Extend the line in both directions to cover the graph.