Question

graph the line.
y = x - 8

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = x - 8 \) 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 \( b=-8 \) (the constant term). This means the line crosses the y - axis at the point \( (0,-8) \) (since when \( x = 0 \), \( y=0 - 8=-8 \)) and has a slope of 1, which means for every 1 unit we move to the right along the x - axis, we move up 1 unit along the y - axis.

Step2: Find a second point

Using the slope, from the y - intercept \( (0,-8) \), if we move 1 unit to the right (increase \( x \) by 1) and 1 unit up (increase \( y \) by 1), we get the point \( (0 + 1,-8+1)=(1,-7) \). We can also find another point by moving in the opposite direction. If we move 1 unit to the left (decrease \( x \) by 1) and 1 unit down (decrease \( y \) by 1) from \( (0,-8) \), we get \( (0 - 1,-8 - 1)=(-1,-9) \).

Step3: Plot the points and draw the line

First, plot the y - intercept \( (0,-8) \) on the coordinate plane. Then plot the second point we found, say \( (1,-7) \) or \( (-1,-9) \). After that, use a straightedge to draw a line through these two points. The line should extend infinitely in both directions.

To graph the line \( y=x - 8 \):

1. Plot the y - intercept at \( (0,-8) \).
2. Use the slope \( m = 1 \) (rise 1, run 1) to find another point (e.g., from \( (0,-8) \), move right 1 and up 1 to get \( (1,-7) \)).
3. Draw a straight line through the plotted points.

(Note: Since the problem is about graphing, the final answer is the graph of the line \( y = x-8 \) with the y - intercept at \( (0, - 8) \) and a slope of 1. If we were to describe the key points, the y - intercept is \( (0,-8) \) and another point could be \( (8,0) \) (by setting \( y = 0 \), we solve \( 0=x - 8\Rightarrow x = 8 \), so the x - intercept is \( (8,0) \)). Plotting \( (0,-8) \) and \( (8,0) \) and drawing a line through them also gives the correct graph.)

Answer:

Step1: Identify the slope and y-intercept

The equation \( y = x - 8 \) 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 \( b=-8 \) (the constant term). This means the line crosses the y - axis at the point \( (0,-8) \) (since when \( x = 0 \), \( y=0 - 8=-8 \)) and has a slope of 1, which means for every 1 unit we move to the right along the x - axis, we move up 1 unit along the y - axis.

Step2: Find a second point

Using the slope, from the y - intercept \( (0,-8) \), if we move 1 unit to the right (increase \( x \) by 1) and 1 unit up (increase \( y \) by 1), we get the point \( (0 + 1,-8+1)=(1,-7) \). We can also find another point by moving in the opposite direction. If we move 1 unit to the left (decrease \( x \) by 1) and 1 unit down (decrease \( y \) by 1) from \( (0,-8) \), we get \( (0 - 1,-8 - 1)=(-1,-9) \).

Step3: Plot the points and draw the line

First, plot the y - intercept \( (0,-8) \) on the coordinate plane. Then plot the second point we found, say \( (1,-7) \) or \( (-1,-9) \). After that, use a straightedge to draw a line through these two points. The line should extend infinitely in both directions.

To graph the line \( y=x - 8 \):

1. Plot the y - intercept at \( (0,-8) \).
2. Use the slope \( m = 1 \) (rise 1, run 1) to find another point (e.g., from \( (0,-8) \), move right 1 and up 1 to get \( (1,-7) \)).
3. Draw a straight line through the plotted points.

(Note: Since the problem is about graphing, the final answer is the graph of the line \( y = x-8 \) with the y - intercept at \( (0, - 8) \) and a slope of 1. If we were to describe the key points, the y - intercept is \( (0,-8) \) and another point could be \( (8,0) \) (by setting \( y = 0 \), we solve \( 0=x - 8\Rightarrow x = 8 \), so the x - intercept is \( (8,0) \)). Plotting \( (0,-8) \) and \( (8,0) \) and drawing a line through them also gives the correct graph.)