Question

graph $y = x - 3$.

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = x - 3 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 1 \) (since the coefficient of \( x \) is 1) and \( b=- 3 \).

Step2: Plot the y-intercept

The y - intercept \( b=-3 \) means the line crosses the y - axis at the point \( (0,-3) \). Locate the point \( (0, - 3) \) on the coordinate plane.

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 \( (0,-3) \), if we move 1 unit to the right (to \( x = 1 \)) and 1 unit up, we get the point \( (1,-2) \). We can also move left 1 unit and down 1 unit from \( (0,-3) \) to get \( (- 1,-4) \).

Step4: Draw the line

Draw a straight line through the points we found (e.g., \( (0,-3) \) and \( (1,-2) \) or other points generated using the slope).

To graph \( y=x - 3 \):

1. Plot the y - intercept at \( (0,-3) \).
2. Use the slope \( m = 1 \) to find another point (e.g., from \( (0,-3) \), move 1 right and 1 up to \( (1,-2) \)).
3. Draw a straight line through these points. The line should have a slope of 1 and pass through \( (0,-3) \), \( (1,-2) \), \( (-1,-4) \), etc.

Answer:

Step1: Identify the slope and y-intercept

The equation \( y = x - 3 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 1 \) (since the coefficient of \( x \) is 1) and \( b=- 3 \).

Step2: Plot the y-intercept

The y - intercept \( b=-3 \) means the line crosses the y - axis at the point \( (0,-3) \). Locate the point \( (0, - 3) \) on the coordinate plane.

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 \( (0,-3) \), if we move 1 unit to the right (to \( x = 1 \)) and 1 unit up, we get the point \( (1,-2) \). We can also move left 1 unit and down 1 unit from \( (0,-3) \) to get \( (- 1,-4) \).

Step4: Draw the line

Draw a straight line through the points we found (e.g., \( (0,-3) \) and \( (1,-2) \) or other points generated using the slope).

To graph \( y=x - 3 \):

1. Plot the y - intercept at \( (0,-3) \).
2. Use the slope \( m = 1 \) to find another point (e.g., from \( (0,-3) \), move 1 right and 1 up to \( (1,-2) \)).
3. Draw a straight line through these points. The line should have a slope of 1 and pass through \( (0,-3) \), \( (1,-2) \), \( (-1,-4) \), etc.