Which Steps Should Be Used To Graph The Equation Below?$y - 4 = \frac{1}{3}(x + 2$\]1. Plot The Point \[$(-2, 4)\$\]. 2. From That Point, Count Right 3 Units And Up 1 Unit, And Plot A Second Point. 3. Draw A Line Through The Two Points.

Understanding the Equation

The given equation is $y - 4 = \frac{1}{3}(x + 2)$. To graph this equation, we need to follow a series of steps that will help us visualize the relationship between the variables $x$ and $y$.

Step 1: Plot the Point

The first step in graphing the equation is to plot the point $(-2, 4)$. This point is obtained by substituting $x = -2$ into the equation and solving for $y$. We get:

$$y - 4 = \frac{1}{3}(-2 + 2)$$

$$y - 4 = \frac{1}{3}(0)$$

$$y - 4 = 0$$

$$y = 4$$

So, the point $(-2, 4)$ lies on the graph of the equation.

Step 2: Count Right 3 Units and Up 1 Unit

From the point $(-2, 4)$, we need to count right 3 units and up 1 unit to plot a second point. To do this, we move 3 units to the right of the point $(-2, 4)$, which gives us the point $(-2 + 3, 4) = (1, 4)$. Then, we move 1 unit up from this point, which gives us the point $(1, 4 + 1) = (1, 5)$.

Step 3: Draw a Line Through the Two Points

The final step in graphing the equation is to draw a line through the two points $(-2, 4)$ and $(1, 5)$. This line represents the graph of the equation $y - 4 = \frac{1}{3}(x + 2)$.

Why This Method Works

The method of graphing the equation by plotting a point and then drawing a line through it works because it is based on the concept of slope. The slope of a line is a measure of how steep it is, and it is calculated as the ratio of the vertical change (rise) to the horizontal change (run). In this case, the slope of the line is $\frac{1}{3}$, which means that for every 3 units we move to the right, we move up 1 unit.

Real-World Applications

Graphing linear equations has many real-world applications, including:

• Physics: Graphing equations of motion is essential in physics to understand the behavior of objects under different forces.
• Engineering: Graphing equations of motion is also crucial in engineering to design and optimize systems.
• Economics: Graphing equations of supply and demand is essential in economics to understand the behavior of markets.

Conclusion

In conclusion, graphing linear equations is a fundamental concept in mathematics that has many real-world applications. By following the steps outlined in this article, you can graph any linear equation and visualize the relationship between the variables $x$ and $y$. Whether you are a student, a teacher, or a professional, graphing linear equations is an essential skill that will serve you well in your future endeavors.

Additional Resources

For more information on graphing linear equations, check out the following resources:

• Mathway: A online math problem solver that can help you graph linear equations.
• Khan Academy: A free online platform that offers video lessons and practice exercises on graphing linear equations.
• Wolfram Alpha: A powerful online calculator that can help you graph linear equations and solve systems of equations.

Frequently Asked Questions

Q: What is the equation of the line that passes through the points $(-2, 4)$ and $(1, 5)$? A: The equation of the line is $y - 4 = \frac{1}{3}(x + 2)$.

Q: How do I graph a linear equation? A: To graph a linear equation, follow the steps outlined in this article: plot a point, count right 3 units and up 1 unit, and draw a line through the two points.

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Frequently Asked Questions

Q: What is the equation of the line that passes through the points $(-2, 4)$ and $(1, 5)$? A: The equation of the line is $y - 4 = \frac{1}{3}(x + 2)$.

Q: How do I graph a linear equation? A: To graph a linear equation, follow the steps outlined in this article: plot a point, count right 3 units and up 1 unit, and draw a line through the two points.

Q: What is the slope of the line that passes through the points $(-2, 4)$ and $(1, 5)$? A: The slope of the line is $\frac{1}{3}$.

Q: How do I find the slope of a line? A: To find the slope of a line, use the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.

Q: What is the y-intercept of the line that passes through the points $(-2, 4)$ and $(1, 5)$? A: The y-intercept of the line is 4.

Q: How do I find the y-intercept of a line? A: To find the y-intercept of a line, use the equation: $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Q: Can I graph a linear equation with a negative slope? A: Yes, you can graph a linear equation with a negative slope. To do this, simply plot a point and then draw a line through it, making sure to move in the opposite direction of the slope.

Q: How do I graph a linear equation with a zero slope? A: To graph a linear equation with a zero slope, simply plot a point and then draw a horizontal line through it.

Q: Can I graph a linear equation with a fractional slope? A: Yes, you can graph a linear equation with a fractional slope. To do this, simply plot a point and then draw a line through it, making sure to move in the correct direction of the slope.

Q: How do I graph a linear equation with a negative fractional slope? A: To graph a linear equation with a negative fractional slope, simply plot a point and then draw a line through it, making sure to move in the opposite direction of the slope.

Q: Can I graph a linear equation with a slope of 1? A: Yes, you can graph a linear equation with a slope of 1. To do this, simply plot a point and then draw a line through it, making sure to move in the correct direction of the slope.

Q: How do I graph a linear equation with a slope of -1? A: To graph a linear equation with a slope of -1, simply plot a point and then draw a line through it, making sure to move in the opposite direction of the slope.

Q: Can I graph a linear equation with a slope of 0? A: Yes, you can graph a linear equation with a slope of 0. To do this, simply plot a point and then draw a horizontal line through it.

Q: How do I graph a linear equation with a negative slope of 0? A: To graph a linear equation with a negative slope of 0, simply plot a point and then draw a horizontal line through it.

Q: Can I graph a linear equation with a fractional slope of 1/2? A: Yes, you can graph a linear equation with a fractional slope of 1/2. To do this, simply plot a point and then draw a line through it, making sure to move in the correct direction of the slope.

Q: How do I graph a linear equation with a negative fractional slope of -1/2? A: To graph a linear equation with a negative fractional slope of -1/2, simply plot a point and then draw a line through it, making sure to move in the opposite direction of the slope.

Conclusion

Graphing linear equations is a fundamental concept in mathematics that has many real-world applications. By following the steps outlined in this article and answering the frequently asked questions, you can graph any linear equation and visualize the relationship between the variables $x$ and $y$. Whether you are a student, a teacher, or a professional, graphing linear equations is an essential skill that will serve you well in your future endeavors.

Additional Resources

For more information on graphing linear equations, check out the following resources:

• Mathway: A online math problem solver that can help you graph linear equations.
• Khan Academy: A free online platform that offers video lessons and practice exercises on graphing linear equations.
• Wolfram Alpha: A powerful online calculator that can help you graph linear equations and solve systems of equations.

Graphing Linear Equations: A Summary

• Plot a point: Plot a point on the graph by substituting a value of $x$ into the equation and solving for $y$.
• Count right 3 units and up 1 unit: Count right 3 units and up 1 unit from the point to plot a second point.
• Draw a line through the two points: Draw a line through the two points to represent the graph of the equation.

Graphing Linear Equations: A Final Note

Graphing linear equations is a fundamental concept in mathematics that has many real-world applications. By following the steps outlined in this article and answering the frequently asked questions, you can graph any linear equation and visualize the relationship between the variables $x$ and $y$. Whether you are a student, a teacher, or a professional, graphing linear equations is an essential skill that will serve you well in your future endeavors.