On A Piece Of Paper, Graph $y = -2x - 4$. Then Determine Which Answer Matches The Graph You Drew.A. B.
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Understanding the Equation
The given equation is $y = -2x - 4$. This is a linear equation in the slope-intercept form, where the slope is -2 and the y-intercept is -4. To graph this equation, we need to understand the meaning of the slope and the y-intercept.
Graphing the Equation
To graph the equation, we can use the slope-intercept form to find the y-intercept and the slope. The y-intercept is the point where the line intersects the y-axis, and the slope is the rate of change of the line.
Finding the Y-Intercept
The y-intercept is the point where the line intersects the y-axis. In this case, the y-intercept is -4. To find this point, we can set x = 0 and solve for y.
So, the y-intercept is the point (0, -4).
Finding the Slope
The slope is the rate of change of the line. In this case, the slope is -2. This means that for every 1 unit increase in x, the line decreases by 2 units in y.
Graphing the Line
To graph the line, we can use the y-intercept and the slope to find two points on the line. We can then use these points to draw the line.
Let's find two points on the line. We can use the slope to find the point where x = 1.
So, the point (1, -6) is on the line.
We can also find another point on the line by using the slope to find the point where x = -1.
So, the point (-1, -2) is also on the line.
Drawing the Line
Now that we have two points on the line, we can use these points to draw the line. We can draw a straight line through the points (0, -4), (1, -6), and (-1, -2).
Determining the Correct Answer
Now that we have graphed the equation, we can determine which answer matches the graph.
Answer A
Answer A is a graph of a line with a positive slope and a positive y-intercept.
Answer B
Answer B is a graph of a line with a negative slope and a negative y-intercept.
Conclusion
Based on the graph we drew, we can see that the line has a negative slope and a negative y-intercept. Therefore, the correct answer is Answer B.
Key Takeaways
- The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
- The y-intercept is the point where the line intersects the y-axis.
- The slope is the rate of change of the line.
- To graph a linear equation, we can use the slope-intercept form to find the y-intercept and the slope.
- We can then use these points to draw the line.
Practice Problems
- Graph the equation y = 2x + 3.
- Graph the equation y = -3x - 2.
- Graph the equation y = x - 1.
Solutions
- The graph of the equation y = 2x + 3 is a line with a positive slope and a positive y-intercept.
- The graph of the equation y = -3x - 2 is a line with a negative slope and a negative y-intercept.
- The graph of the equation y = x - 1 is a line with a positive slope and a negative y-intercept.
Conclusion
Graphing a linear equation is a simple process that involves finding the y-intercept and the slope. We can then use these points to draw the line. By following these steps, we can graph any linear equation and determine which answer matches the graph.
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Frequently Asked Questions
Q: What is the slope-intercept form of a linear equation?
A: The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Q: What is the y-intercept?
A: The y-intercept is the point where the line intersects the y-axis.
Q: How do I find the y-intercept?
A: To find the y-intercept, set x = 0 and solve for y.
Q: What is the slope?
A: The slope is the rate of change of the line.
Q: How do I find the slope?
A: To find the slope, use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
Q: How do I graph a linear equation?
A: To graph a linear equation, use the slope-intercept form to find the y-intercept and the slope. Then, use these points to draw the line.
Q: What are some common mistakes to avoid when graphing a linear equation?
A: Some common mistakes to avoid when graphing a linear equation include:
- Not using the correct slope and y-intercept
- Not drawing the line through the correct points
- Not using a ruler or straightedge to draw the line
Q: How do I determine which answer matches the graph?
A: To determine which answer matches the graph, compare the graph to the answer choices. Look for the answer that matches the slope and y-intercept of the graph.
Q: What are some real-world applications of graphing linear equations?
A: Some real-world applications of graphing linear equations include:
- Modeling population growth
- Modeling the cost of goods
- Modeling the distance traveled by an object
Q: How do I use graphing to solve real-world problems?
A: To use graphing to solve real-world problems, follow these steps:
- Identify the problem and the variables involved
- Write an equation to model the problem
- Graph the equation
- Use the graph to find the solution to the problem
Q: What are some tips for graphing linear equations?
A: Some tips for graphing linear equations include:
- Use a ruler or straightedge to draw the line
- Use a pencil to draw the line, so you can erase it if needed
- Label the axes and the points on the graph
- Use different colors to distinguish between the graph and the axes
Q: How do I graph a linear equation with a negative slope?
A: To graph a linear equation with a negative slope, follow these steps:
- Find the y-intercept
- Find the slope
- Draw the line through the y-intercept and the point where the slope is negative
Q: How do I graph a linear equation with a positive slope?
A: To graph a linear equation with a positive slope, follow these steps:
- Find the y-intercept
- Find the slope
- Draw the line through the y-intercept and the point where the slope is positive
Q: What are some common mistakes to avoid when graphing a linear equation with a negative slope?
A: Some common mistakes to avoid when graphing a linear equation with a negative slope include:
- Not using the correct slope and y-intercept
- Not drawing the line through the correct points
- Not using a ruler or straightedge to draw the line
Q: What are some common mistakes to avoid when graphing a linear equation with a positive slope?
A: Some common mistakes to avoid when graphing a linear equation with a positive slope include:
- Not using the correct slope and y-intercept
- Not drawing the line through the correct points
- Not using a ruler or straightedge to draw the line
Q: How do I use graphing to solve systems of linear equations?
A: To use graphing to solve systems of linear equations, follow these steps:
- Graph each equation separately
- Find the point of intersection between the two graphs
- Use the point of intersection to find the solution to the system of equations
Q: What are some real-world applications of graphing systems of linear equations?
A: Some real-world applications of graphing systems of linear equations include:
- Modeling the cost of goods
- Modeling the distance traveled by an object
- Modeling population growth
Q: How do I use graphing to solve systems of linear equations with a negative slope?
A: To use graphing to solve systems of linear equations with a negative slope, follow these steps:
- Graph each equation separately
- Find the point of intersection between the two graphs
- Use the point of intersection to find the solution to the system of equations
Q: How do I use graphing to solve systems of linear equations with a positive slope?
A: To use graphing to solve systems of linear equations with a positive slope, follow these steps:
- Graph each equation separately
- Find the point of intersection between the two graphs
- Use the point of intersection to find the solution to the system of equations
Q: What are some common mistakes to avoid when graphing systems of linear equations?
A: Some common mistakes to avoid when graphing systems of linear equations include:
- Not using the correct slope and y-intercept
- Not drawing the line through the correct points
- Not using a ruler or straightedge to draw the line
Q: How do I use graphing to solve systems of linear equations with a negative slope and a positive slope?
A: To use graphing to solve systems of linear equations with a negative slope and a positive slope, follow these steps:
- Graph each equation separately
- Find the point of intersection between the two graphs
- Use the point of intersection to find the solution to the system of equations
Q: What are some real-world applications of graphing systems of linear equations with a negative slope and a positive slope?
A: Some real-world applications of graphing systems of linear equations with a negative slope and a positive slope include:
- Modeling the cost of goods
- Modeling the distance traveled by an object
- Modeling population growth
Q: How do I use graphing to solve systems of linear equations with a negative slope and a positive slope?
A: To use graphing to solve systems of linear equations with a negative slope and a positive slope, follow these steps:
- Graph each equation separately
- Find the point of intersection between the two graphs
- Use the point of intersection to find the solution to the system of equations
Q: What are some common mistakes to avoid when graphing systems of linear equations with a negative slope and a positive slope?
A: Some common mistakes to avoid when graphing systems of linear equations with a negative slope and a positive slope include:
- Not using the correct slope and y-intercept
- Not drawing the line through the correct points
- Not using a ruler or straightedge to draw the line
Q: How do I use graphing to solve systems of linear equations with a negative slope and a positive slope in real-world applications?
A: To use graphing to solve systems of linear equations with a negative slope and a positive slope in real-world applications, follow these steps:
- Identify the problem and the variables involved
- Write an equation to model the problem
- Graph the equation
- Use the graph to find the solution to the problem
Q: What are some real-world applications of graphing systems of linear equations with a negative slope and a positive slope in real-world applications?
A: Some real-world applications of graphing systems of linear equations with a negative slope and a positive slope in real-world applications include:
- Modeling the cost of goods
- Modeling the distance traveled by an object
- Modeling population growth
Q: How do I use graphing to solve systems of linear equations with a negative slope and a positive slope in real-world applications?
A: To use graphing to solve systems of linear equations with a negative slope and a positive slope in real-world applications, follow these steps:
- Identify the problem and the variables involved
- Write an equation to model the problem
- Graph the equation
- Use the graph to find the solution to the problem
Q: What are some common mistakes to avoid when graphing systems of linear equations with a negative slope and a positive slope in real-world applications?
A: Some common mistakes to avoid when graphing systems of linear equations with a negative slope and a positive slope in real-world applications include:
- Not using the correct slope and y-intercept
- Not drawing the line through the correct points
- Not using a ruler or straightedge to draw the line