What Is The Equation, In Slope-intercept Form, Of The Line That Passes Through { (0, -2)$}$ And Has A Slope Of { -3$}$?A. { Y = -3x - 2$}$ B. { Y = -3x + 2$}$ C. { Y = -2x + 3$}$ D. [$y = -2x -
Understanding Slope-Intercept Form
The slope-intercept form of a line is a mathematical equation that represents a line on a coordinate plane. It is written in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. The slope-intercept form is a useful way to represent a line because it allows us to easily identify the slope and y-intercept of the line.
The Equation of a Line in Slope-Intercept Form
To find the equation of a line in slope-intercept form, we need to know the slope and y-intercept of the line. The slope of a line is a measure of how steep the line is, and it is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. The y-intercept of a line is the point where the line intersects the y-axis.
Finding the Equation of a Line
To find the equation of a line in slope-intercept form, we can use the following formula:
y = mx + b
where m is the slope of the line and b is the y-intercept.
Example: Finding the Equation of a Line
Let's say we have a line that passes through the point (0, -2) and has a slope of -3. We can use the slope-intercept form of the equation to find the equation of the line.
Step 1: Write the Equation in Slope-Intercept Form
The equation of a line in slope-intercept form is y = mx + b. We know that the slope of the line is -3, so we can write the equation as:
y = -3x + b
Step 2: Find the Y-Intercept
We know that the line passes through the point (0, -2), so we can substitute x = 0 and y = -2 into the equation to find the y-intercept.
-2 = -3(0) + b
Simplifying the equation, we get:
-2 = b
So, the y-intercept of the line is -2.
Step 3: Write the Final Equation
Now that we have found the y-intercept, we can write the final equation of the line in slope-intercept form.
y = -3x - 2
Conclusion
In this article, we have learned how to find the equation of a line in slope-intercept form. We have used the slope-intercept form of the equation to find the equation of a line that passes through the point (0, -2) and has a slope of -3. The final equation of the line is y = -3x - 2.
Discussion
What is the equation of a line in slope-intercept form? How do you find the equation of a line in slope-intercept form? What are some common applications of the slope-intercept form of a line?
Answer Key
A. y = -3x - 2 B. y = -3x + 2 C. y = -2x + 3 D. y = -2x - 3
The correct answer is A. y = -3x - 2.
Additional Resources
For more information on the slope-intercept form of a line, please see the following resources:
- Slope-Intercept Form of a Line
- [Equation of a Line](https://www.khanacademy.org/math/algebra/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8
Q&A: What is the Equation of a Line in Slope-Intercept Form? ===========================================================
Q: What is the slope-intercept form of a line?
A: The slope-intercept form of a line is a mathematical equation that represents a line on a coordinate plane. It is written in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.
Q: How do I find the equation of a line in slope-intercept form?
A: To find the equation of a line in slope-intercept form, you need to know the slope and y-intercept of the line. The slope of a line is a measure of how steep the line is, and it is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. The y-intercept of a line is the point where the line intersects the y-axis.
Q: What is the slope of a line?
A: The slope of a line is a measure of how steep the line is. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.
Q: How do I calculate the slope of a line?
A: To calculate the slope of a line, you need to know the coordinates of two points on the line. The slope is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between the two points.
Q: What is the y-intercept of a line?
A: The y-intercept of a line is the point where the line intersects the y-axis. It is the value of y when x is equal to zero.
Q: How do I find the y-intercept of a line?
A: To find the y-intercept of a line, you need to know the equation of the line in slope-intercept form. The y-intercept is the value of b in the equation y = mx + b.
Q: What is the equation of a line in slope-intercept form?
A: The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.
Q: How do I write the equation of a line in slope-intercept form?
A: To write the equation of a line in slope-intercept form, you need to know the slope and y-intercept of the line. The equation is written in the form of y = mx + b, where m is the slope and b is the y-intercept.
Q: What are some common applications of the slope-intercept form of a line?
A: The slope-intercept form of a line is used in a variety of applications, including:
- Calculating the slope and y-intercept of a line
- Writing the equation of a line in slope-intercept form
- Graphing a line on a coordinate plane
- Finding the equation of a line that passes through two points
- Finding the equation of a line that is parallel or perpendicular to another line
Q: What are some common mistakes to avoid when working with the slope-intercept form of a line?
A: Some common mistakes to avoid when working with the slope-intercept form of a line include:
- Confusing the slope and y-intercept
- Writing the equation of a line in the wrong form
- Failing to calculate the slope and y-intercept correctly
- Failing to check the equation of a line for errors
Conclusion
In this article, we have answered some common questions about the slope-intercept form of a line. We have discussed the slope and y-intercept of a line, how to calculate the slope and y-intercept, and how to write the equation of a line in slope-intercept form. We have also discussed some common applications of the slope-intercept form of a line and some common mistakes to avoid when working with it.
Additional Resources
For more information on the slope-intercept form of a line, please see the following resources:
- Slope-Intercept Form of a Line
- [Equation of a Line](https://www.khanacademy.org/math/algebra/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f8c7d7/x2f