Question

graph the line with the equation $y = 2x - 2$.

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = 2x - 2 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 2 \) (which can be written as \( \frac{2}{1} \)) and \( b=- 2 \). So the line crosses the y - axis at \( (0,-2) \).

Step2: Plot the y - intercept

Locate the point \( (0,-2) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m = \frac{2}{1} \) means that from the y - intercept \( (0,-2) \), we move up 2 units and then 1 unit to the right. Moving up 2 units from \( y=-2 \) gives \( y=-2 + 2=0 \), and moving 1 unit to the right from \( x = 0 \) gives \( x=0 + 1 = 1 \). So we get the point \( (1,0) \). We can also move down 2 units and left 1 unit from the y - intercept: moving down 2 units from \( y=-2 \) gives \( y=-2-2=-4 \), and moving left 1 unit from \( x = 0 \) gives \( x=0 - 1=-1 \), so we get the point \( (-1,-4) \).

Step4: Draw the line

Connect the points (for example, \( (0,-2) \), \( (1,0) \)) with a straight line. If we want to check the point given in the graph (the blue dot at \( (-3,9) \)): substitute \( x=-3 \) into the equation \( y = 2x-2 \), we get \( y=2\times(-3)-2=-6 - 2=-8
eq9 \), so that point is not on the line \( y = 2x-2 \). The correct line should pass through points like \( (0,-2) \), \( (1,0) \), \( (-1,-4) \) etc.

Answer:

To graph \( y = 2x-2 \):

1. Plot the y - intercept \( (0,-2) \).
2. Use the slope \( m = 2 \) to find another point (e.g., from \( (0,-2) \), move up 2, right 1 to get \( (1,0) \)).
3. Draw a straight line through these points. The line should pass through \( (0,-2) \), \( (1,0) \), \( (-1,-4) \) etc., and not through the pre - plotted point \( (-3,9) \) (since substituting \( x = - 3 \) into \( y=2x - 2 \) gives \( y=-8

eq9 \)).