To graph the equation [tex]\( y = -2x - 3 \)[/tex] and find the correct match, follow these steps:
### Step 1: Identify the slope and y-intercept
The given equation is in slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- Here, the slope ([tex]\( m \)[/tex]) is -2.
- The y-intercept ([tex]\( b \)[/tex]) is -3.
### Step 2: Plot the y-intercept
The y-intercept is the point where the line crosses the y-axis. For [tex]\( y = -2x - 3 \)[/tex]:
- Start at the y-intercept, which is [tex]\((0, -3)\)[/tex]. Plot this point on the y-axis.
### Step 3: Use the slope to find another point
The slope of -2 means that for every 1 unit increase in [tex]\( x \)[/tex], [tex]\( y \)[/tex] decreases by 2 units.
- Starting from the y-intercept [tex]\((0, -3)\)[/tex], move 1 unit right ([tex]\( x \)[/tex] increases by 1).
- Since the slope is -2, move 2 units down ([tex]\( y \)[/tex] decreases by 2).
This gives you a new point:
- From [tex]\((0, -3)\)[/tex], moving 1 unit right and 2 units down lands you at [tex]\((1, -5)\)[/tex]. Plot this point as well.
### Step 4: Draw the line
- Draw a straight line through the points [tex]\((0, -3)\)[/tex] and [tex]\((1, -5)\)[/tex].
### Step 5: Determine if additional points follow the line
To ensure accuracy, let's find another point using the slope again:
- From [tex]\((1, -5)\)[/tex], moving 1 unit right and 2 units down gets you to [tex]\((2, -7)\)[/tex]. Plot this point if needed for accuracy.
### Step 6: Match with the provided options
- Compare the graph you have drawn with the provided multiple-choice options (A, B, etc.) to see which one matches the line passing through the points [tex]\((0, -3)\)[/tex], [tex]\((1, -5)\)[/tex], and possibly [tex]\((2, -7)\)[/tex].
Unfortunately, options A and B are not fully provided here, so it's not possible to match directly. However, upon drawing the graph, it should be clear by visually comparing with the provided options which one is correct. Look for the option where the line passes through the mentioned intercept and points based on the slope discussed.
