Question

graph the line with the equation $y = x - 4$.

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = x - 4 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 1 \) (the coefficient of \( x \)) and \( b=-4 \) (the constant term).

Step2: Plot the y - intercept

The y - intercept is \( b=-4 \), so we plot the point \( (0,-4) \) on the y - axis.

Step3: Use the slope to find another point

The slope \( m = 1=\frac{1}{1} \), which means for every 1 unit we move to the right (increase in \( x \) by 1), we move up 1 unit (increase in \( y \) by 1). Starting from \( (0,-4) \), if we move 1 unit to the right (to \( x = 1 \)) and 1 unit up, we get the point \( (1,-3) \). We can also move left 1 unit and down 1 unit from \( (0,-4) \) to get \( (-1,-5) \).

Step4: Draw the line

Draw a straight line through the points we have plotted (e.g., \( (0,-4) \), \( (1,-3) \), \( (-1,-5) \)) to graph the line \( y=x - 4 \).

Answer:

To graph \( y=x - 4 \):

1. Plot the y - intercept at \( (0,-4) \).
2. Use the slope \( m = 1 \) to find another point (e.g., \( (1,-3) \) by moving 1 right and 1 up from \( (0,-4) \)).
3. Draw a straight line through these points. The line should pass through points like \( (0,-4) \), \( (1,-3) \), \( (2,-2) \), etc., and extend in both directions. (Note: The actual graph is a straight line with a slope of 1 and y - intercept at - 4 on the coordinate plane.)