Question

advanced graphing practice

1. $y = x - 5$
2. $y = (x - 5)$
3. $y = (x + 6) - 8$
4. $y = (x - 8) + 7$

Explanation:

Step1: Analyze the equation form

The equation \( y = x - 5 \) (or simplified as \( y=(x - 5) \)) is a linear equation in the form \( y=mx + b \), where \( m = 1 \) (slope) and \( b=- 5 \) (y - intercept). For a linear equation \( y=mx + b \), the graph is a straight line with slope \( m \) and y - intercept at \( (0,b) \). Also, we can find the x - intercept by setting \( y = 0 \), so \( 0=x - 5\Rightarrow x = 5 \), so the x - intercept is at \( (5,0) \) and y - intercept at \( (0,-5) \).

Step2: Check the given graph (first graph)

The first graph has a vertical line? No, wait, the red line in the first graph seems to be a vertical line, but our equation \( y=x - 5 \) is a non - vertical line (slope 1). Wait, maybe there was a mistake in the initial graphing. But if we consider the correct graph for \( y=x - 5 \):

• The slope is 1, so for every 1 unit we move to the right (in x - direction), we move 1 unit up (in y - direction).
• The y - intercept is at \( (0,-5) \) and x - intercept at \( (5,0) \).

For the second equation \( y=(x - 5) \) (same as \( y=x - 5 \)):

• We can plot two points. When \( x = 0 \), \( y=-5 \); when \( y = 0 \), \( x = 5 \). Then draw a straight line through these two points.

For the equation \( y=(x + 6)-8=x - 2 \):

• Slope \( m = 1 \), y - intercept \( b=-2 \) (when \( x = 0 \), \( y=-2 \)), x - intercept: \( 0=x - 2\Rightarrow x = 2 \) (when \( y = 0 \)).

For the equation \( y=(x - 8)+7=x - 1 \):

• Slope \( m = 1 \), y - intercept \( b=-1 \) (when \( x = 0 \), \( y=-1 \)), x - intercept: \( 0=x - 1\Rightarrow x = 1 \) (when \( y = 0 \)).

Let's take the first equation \( y=x - 5 \):

• To graph it, start at the y - intercept \( (0,-5) \). Then, since the slope is 1 (rise over run \( \frac{1}{1} \)), from \( (0,-5) \), move 1 unit right and 1 unit up to get \( (1,-4) \), another unit right and up to \( (2,-3) \), and so on. Also, from \( (0,-5) \), move 1 unit left and 1 unit down to \( (-1,-6) \).

If we check the first graph (top - left), the red line is vertical, which is incorrect for \( y=x - 5 \) (a non - vertical line with slope 1). The correct graph for \( y=x - 5 \) should be a straight line with slope 1 passing through \( (0,-5) \) and \( (5,0) \).

Answer:

To graph \( y=x - 5 \) (or \( y=(x - 5) \)):

1. Plot the y - intercept at \( (0,-5) \).
2. Plot the x - intercept at \( (5,0) \).
3. Draw a straight line through these two points.

To graph \( y=(x + 6)-8=x - 2 \):

1. Plot the y - intercept at \( (0,-2) \).
2. Plot the x - intercept at \( (2,0) \).
3. Draw a straight line through these two points.

To graph \( y=(x - 8)+7=x - 1 \):

1. Plot the y - intercept at \( (0,-1) \).
2. Plot the x - intercept at \( (1,0) \).
3. Draw a straight line through these two points.