To identify the correct graph of the equation \( y = 2x - 3 \), let's analyze the equation step-by-step:
1. Identify the y-intercept:
The equation \( y = 2x - 3 \) is in slope-intercept form \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept. Here, the y-intercept \( b \) is -3. This means the line crosses the y-axis at the point \( (0, -3) \).
2. Identify the slope:
The slope \( m \) is 2. This tells us that for every 1 unit increase in \( x \), \( y \) increases by 2 units. This rise over run creates a line that moves upwards steeply.
3. Plotting the line:
Let's start at the y-intercept \( (0, -3) \). From this point:
- Move 1 unit to the right (positive x-direction).
- Move 2 units up (positive y-direction).
This will give us another point on the line, \( (1, -1) \).
4. Construct the line:
Draw a straight line through the points \( (0, -3) \) and \( (1, -1) \). This line will continue infinitely in both directions.
Now we compare these details with the provided options (A, B, C, D):
- The correct graph will cross the y-axis at \( (0, -3) \).
- It will have a positive and consistent upward slope of 2.
Given these characteristics, look at the graphs of the options provided and match them with these criteria.
The correct graph will be represented by the option that meets all the requirements:
- A line crossing the y-axis at \( (0, -3) \).
- A line with a slope of 2 (steeply rising).
Identify the graph properly with these steps, and you will have the option that correctly represents the equation [tex]\( y = 2x - 3 \)[/tex].
