Line { CD $}$ Passes Through The Points { (0, 2)$}$ And { (4, 6)$}$. Which Equation Represents Line { CD $}$?A. { Y = 2x - 2 $}$B. { Y = 2x + 2 $}$C. { Y = X + 2 $} D . \[ D. \[ D . \[ Y
Introduction
In mathematics, a line is a set of points that extend infinitely in two directions. The equation of a line is a mathematical expression that describes the relationship between the x and y coordinates of any point on the line. In this article, we will discuss how to find the equation of a line passing through two given points.
The Problem
We are given two points, (0, 2) and (4, 6), and we need to find the equation of the line that passes through these two points. The line is represented by the symbol CD.
The Solution
To find the equation of the line, we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept.
Finding the Slope
The slope of a line is a measure of how steep it is. It can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
In this case, we have two points, (0, 2) and (4, 6). We can plug these values into the formula to find the slope:
m = (6 - 2) / (4 - 0) m = 4 / 4 m = 1
Finding the Y-Intercept
The y-intercept is the point where the line intersects the y-axis. In this case, we know that the line passes through the point (0, 2), so the y-intercept is 2.
Writing the Equation
Now that we have the slope and the y-intercept, we can write the equation of the line in slope-intercept form:
y = mx + b y = 1x + 2 y = x + 2
Conclusion
In this article, we discussed how to find the equation of a line passing through two given points. We used the slope-intercept form of a linear equation and calculated the slope and y-intercept using the given points. The equation of the line is y = x + 2.
Answer
The correct answer is:
C. y = x + 2
Other Options
Let's take a look at the other options:
A. y = 2x - 2
This equation has a slope of 2, which is not equal to the slope we calculated earlier.
B. y = 2x + 2
This equation has a slope of 2, which is not equal to the slope we calculated earlier.
D. y = x - 2
This equation has a slope of 1, but the y-intercept is -2, which is not equal to the y-intercept we calculated earlier.
Final Answer
Introduction
In our previous article, we discussed how to find the equation of a line passing through two given points. In this article, we will provide a Q&A guide to help you better understand the concept.
Q: What is the equation of a line?
A: The equation of a line is a mathematical expression that describes the relationship between the x and y coordinates of any point on the line.
Q: What is the slope of a line?
A: The slope of a line is a measure of how steep it is. It can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
Q: How do I find the slope of a line?
A: To find the slope of a line, you can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
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.
Q: How do I find the y-intercept of a line?
A: To find the y-intercept of a line, you can use the point where the line intersects the y-axis.
Q: What is the equation of a line in slope-intercept form?
A: The equation of a line in slope-intercept form is given by:
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 the y-intercept of the line.
Q: What is the equation of the line CD?
A: The equation of the line CD is y = x + 2.
Q: Why is the equation of the line CD y = x + 2?
A: The equation of the line CD is y = x + 2 because the slope of the line is 1 and the y-intercept is 2.
Q: Can I use the equation of the line CD to find the coordinates of any point on the line?
A: Yes, you can use the equation of the line CD to find the coordinates of any point on the line.
Q: How do I use the equation of the line CD to find the coordinates of any point on the line?
A: To use the equation of the line CD to find the coordinates of any point on the line, you need to plug in the x-coordinate of the point into the equation and solve for the y-coordinate.
Q: What are some common mistakes to avoid when finding the equation of a line?
A: Some common mistakes to avoid when finding the equation of a line include:
- Not using the correct formula for the slope
- Not using the correct formula for the y-intercept
- Not plugging in the correct values into the equation
- Not solving for the correct variable
Conclusion
In this article, we provided a Q&A guide to help you better understand the concept of finding the equation of a line. We discussed the equation of a line, the slope of a line, the y-intercept of a line, and how to write the equation of a line in slope-intercept form. We also provided some common mistakes to avoid when finding the equation of a line.