Question

question graph the line with the equation $y = x - 3$.

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, \( m = 1 \) (the coefficient of \( x \)) and \( b=-3 \) (the constant term). This means the line crosses the y - axis at the point \( (0,-3) \) (since when \( x = 0 \), \( y=0 - 3=-3 \)).

Step2: 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 the y - intercept \( (0,-3) \), if we move 1 unit to the right ( \( x = 0+1 = 1 \)) and 1 unit up ( \( y=-3 + 1=-2 \)), we get the point \( (1,-2) \). We can also move in the opposite direction: from \( (0,-3) \), move 1 unit to the left ( \( x=0 - 1=-1 \)) and 1 unit down ( \( y=-3-1=-4 \)) to get the point \( (-1,-4) \).

Step3: Plot the points and draw the line

Plot the points \( (0,-3) \), \( (1,-2) \), \( (-1,-4) \) (or any other points found using the slope) on the coordinate plane. Then, draw a straight line through these points. The line should have a positive slope (going up from left to right) and pass through the y - axis at \( (0,-3) \).

(Note: Since the problem is about graphing, the final answer is the graph of the line \( y=x - 3 \) with the correct points plotted and the line drawn as per the steps above. If we were to describe the key points, the y - intercept is \( (0,-3) \) and another point can be \( (1,-2) \) etc.)

Answer:

The graph of the line \( y = x-3 \) has a y - intercept at \( (0, - 3) \) and a slope of 1. It passes through points like \( (0,-3) \), \( (1,-2) \), \( (2,-1) \), etc., and is a straight line with a positive slope. (To draw it, plot \( (0,-3) \), then use the slope of 1 to find other points and connect them.)