Question

graph the following equation.
$y = x - 4$
show your work here

Explanation:

Step1: Identify the form of the equation

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

Step2: Find the y - intercept

The y - intercept is the point where the line crosses the y - axis. When \( x = 0 \), we substitute \( x = 0 \) into the equation \( y=x - 4 \). So \( y=0 - 4=-4 \). So the y - intercept is the point \( (0,-4) \).

Step3: Use the slope to find another point

The slope \( m = 1=\frac{1}{1}=\frac{\text{rise}}{\text{run}} \). Starting from the y - intercept \( (0,-4) \), we move up 1 unit (because the rise is 1) and then move to the right 1 unit (because the run is 1). This gives us the point \( (0 + 1,-4 + 1)=(1,-3) \).

Step4: Draw the line

Plot the points \( (0,-4) \) and \( (1,-3) \) (and we can find more points by repeating the slope - based movement if needed) and then draw a straight line passing through these points.

(Note: Since the problem asks to graph the equation, the final answer is the graph of the line \( y=x - 4 \) passing through points like \( (0,-4) \), \( (1,-3) \), \( (2,-2) \) etc. If we were to describe the key points for graphing, the y - intercept is \( (0,-4) \) and another point is \( (1,-3) \) and the line has a slope of 1.)

Answer:

Step1: Identify the form of the equation

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

Step2: Find the y - intercept

The y - intercept is the point where the line crosses the y - axis. When \( x = 0 \), we substitute \( x = 0 \) into the equation \( y=x - 4 \). So \( y=0 - 4=-4 \). So the y - intercept is the point \( (0,-4) \).

Step3: Use the slope to find another point

The slope \( m = 1=\frac{1}{1}=\frac{\text{rise}}{\text{run}} \). Starting from the y - intercept \( (0,-4) \), we move up 1 unit (because the rise is 1) and then move to the right 1 unit (because the run is 1). This gives us the point \( (0 + 1,-4 + 1)=(1,-3) \).

Step4: Draw the line

Plot the points \( (0,-4) \) and \( (1,-3) \) (and we can find more points by repeating the slope - based movement if needed) and then draw a straight line passing through these points.

(Note: Since the problem asks to graph the equation, the final answer is the graph of the line \( y=x - 4 \) passing through points like \( (0,-4) \), \( (1,-3) \), \( (2,-2) \) etc. If we were to describe the key points for graphing, the y - intercept is \( (0,-4) \) and another point is \( (1,-3) \) and the line has a slope of 1.)