Choose The Most Convenient Method To Graph The Line $x-y=5$.Select The Correct Answer Below:A. Recognize The Equation As That Of A Vertical Line Passing Through The $x$-axis At 5.B. Recognize The Equation As That Of A Horizontal
Understanding the Basics of Graphing Lines
Graphing lines is a fundamental concept in mathematics, and it's essential to understand the different methods to graph lines accurately. In this article, we will explore the most convenient method to graph the line $x-y=5$ and discuss the correct answer among the given options.
Option A: Recognize the Equation as a Vertical Line
The equation $x-y=5$ can be rewritten as $x=5+y$. This equation represents a vertical line passing through the $x$-axis at $x=5$. To graph this line, we need to plot a point on the $x$-axis at $x=5$ and draw a vertical line passing through that point.
Option B: Recognize the Equation as a Horizontal Line
The equation $x-y=5$ can also be rewritten as $y=x-5$. This equation represents a horizontal line passing through the $y$-axis at $y=-5$. To graph this line, we need to plot a point on the $y$-axis at $y=-5$ and draw a horizontal line passing through that point.
The Correct Answer
The correct answer is Option A: Recognize the equation as a vertical line passing through the $x$-axis at 5. This is because the equation $x-y=5$ represents a vertical line passing through the $x$-axis at $x=5$.
Why is this the Correct Answer?
The equation $x-y=5$ can be rewritten as $x=5+y$. This equation represents a vertical line passing through the $x$-axis at $x=5$. To graph this line, we need to plot a point on the $x$-axis at $x=5$ and draw a vertical line passing through that point. This is the most convenient method to graph the line $x-y=5$.
Graphing Lines: A Step-by-Step Guide
Step 1: Rewrite the Equation
The first step in graphing a line is to rewrite the equation in the slope-intercept form, $y=mx+b$. The equation $x-y=5$ can be rewritten as $y=x-5$.
Step 2: Identify the Slope and Y-Intercept
The slope of the line is the coefficient of $x$, which is 1. The y-intercept is the constant term, which is -5.
Step 3: Plot the Y-Intercept
To graph the line, we need to plot the y-intercept, which is the point where the line intersects the y-axis. In this case, the y-intercept is (-5, 0).
Step 4: Draw the Line
Once we have plotted the y-intercept, we can draw the line by using a ruler or a straightedge. The line should be drawn at a 45-degree angle, since the slope is 1.
Step 5: Check the Graph
Finally, we need to check the graph to make sure it is accurate. We can do this by plugging in a few test points into the equation and checking if they lie on the line.
Conclusion
Graphing lines is a fundamental concept in mathematics, and it's essential to understand the different methods to graph lines accurately. In this article, we explored the most convenient method to graph the line $x-y=5$ and discussed the correct answer among the given options. We also provided a step-by-step guide on how to graph lines, including rewriting the equation, identifying the slope and y-intercept, plotting the y-intercept, drawing the line, and checking the graph.
Frequently Asked Questions
Q: What is the most convenient method to graph the line $x-y=5$?
A: The most convenient method to graph the line $x-y=5$ is to recognize the equation as a vertical line passing through the $x$-axis at $x=5$.
Q: How do I graph a line?
A: To graph a line, you need to rewrite the equation in the slope-intercept form, identify the slope and y-intercept, plot the y-intercept, draw the line, and check the graph.
Q: What is the slope-intercept form of a line?
A: The slope-intercept form of a line is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.
Q: How do I identify the slope and y-intercept of a line?
A: To identify the slope and y-intercept of a line, you need to rewrite the equation in the slope-intercept form and look at the coefficients of $x$ and the constant term.
References
- [1] "Graphing Lines" by Math Open Reference
- [2] "Slope-Intercept Form" by Khan Academy
- [3] "Graphing Lines" by Purplemath
Graphing Lines: A Q&A Guide =============================
Frequently Asked Questions
Q: What is the most convenient method to graph the line $x-y=5$?
A: The most convenient method to graph the line $x-y=5$ is to recognize the equation as a vertical line passing through the $x$-axis at $x=5$.
Q: How do I graph a line?
A: To graph a line, you need to rewrite the equation in the slope-intercept form, identify the slope and y-intercept, plot the y-intercept, draw the line, and check the graph.
Q: What is the slope-intercept form of a line?
A: The slope-intercept form of a line is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.
Q: How do I identify the slope and y-intercept of a line?
A: To identify the slope and y-intercept of a line, you need to rewrite the equation in the slope-intercept form and look at the coefficients of $x$ and the constant term.
Q: What is the difference between a vertical and horizontal line?
A: A vertical line is a line that passes through the $x$-axis at a specific point, while a horizontal line is a line that passes through the $y$-axis at a specific point.
Q: How do I graph a vertical line?
A: To graph a vertical line, you need to plot a point on the $x$-axis at the specific point where the line passes through, and then draw a vertical line passing through that point.
Q: How do I graph a horizontal line?
A: To graph a horizontal line, you need to plot a point on the $y$-axis at the specific point where the line passes through, and then draw a horizontal line passing through that point.
Q: What is the equation of a line that passes through the points $(2,3)$ and $(4,5)$?
A: To find the equation of a line that passes through two points, you need to use the point-slope form of a line, which is $y-y_1=m(x-x_1)$. Plugging in the points $(2,3)$ and $(4,5)$, we get $y-3=m(x-2)$ and $y-5=m(x-4)$. Equating the two expressions, we get $m(x-2)=m(x-4)+2$. Simplifying, we get $m=2$. Plugging this value back into one of the original equations, we get $y-3=2(x-2)$. Simplifying, we get $y=2x-1$.
Q: How do I find the equation of a line that passes through a point and has a given slope?
A: To find the equation of a line that passes through a point and has a given slope, you need to use the point-slope form of a line, which is $y-y_1=m(x-x_1)$. Plugging in the point and the slope, you can solve for the equation of the line.
Q: What is the equation of a line that passes through the point $(2,3)$ and has a slope of $2$?
A: Using the point-slope form of a line, we get $y-3=2(x-2)$. Simplifying, we get $y=2x-1$.
Q: How do I find the equation of a line that passes through two points?
A: To find the equation of a line that passes through two points, you need to use the point-slope form of a line, which is $y-y_1=m(x-x_1)$. Plugging in the two points, you can solve for the equation of the line.
Q: What is the equation of a line that passes through the points $(2,3)$ and $(4,5)$?
A: Using the point-slope form of a line, we get $y-3=m(x-2)$ and $y-5=m(x-4)$. Equating the two expressions, we get $m(x-2)=m(x-4)+2$. Simplifying, we get $m=2$. Plugging this value back into one of the original equations, we get $y-3=2(x-2)$. Simplifying, we get $y=2x-1$.
Conclusion
Graphing lines is a fundamental concept in mathematics, and it's essential to understand the different methods to graph lines accurately. In this article, we provided a Q&A guide on graphing lines, including the most convenient method to graph the line $x-y=5$, how to graph a line, what is the slope-intercept form of a line, how to identify the slope and y-intercept of a line, and more.
Frequently Asked Questions
Q: What is the most convenient method to graph the line $x-y=5$?
A: The most convenient method to graph the line $x-y=5$ is to recognize the equation as a vertical line passing through the $x$-axis at $x=5$.
Q: How do I graph a line?
A: To graph a line, you need to rewrite the equation in the slope-intercept form, identify the slope and y-intercept, plot the y-intercept, draw the line, and check the graph.
Q: What is the slope-intercept form of a line?
A: The slope-intercept form of a line is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.
Q: How do I identify the slope and y-intercept of a line?
A: To identify the slope and y-intercept of a line, you need to rewrite the equation in the slope-intercept form and look at the coefficients of $x$ and the constant term.
References
- [1] "Graphing Lines" by Math Open Reference
- [2] "Slope-Intercept Form" by Khan Academy
- [3] "Graphing Lines" by Purplemath