The Graph Of A Line Passes Through The Points \[$(0, -2)\$\] And \[$(6, 0)\$\]. What Is The Equation Of The Line?A. \[$y = -2x + 6\$\] B. \[$y = \frac{1}{3}x - 6\$\] C. \[$y = 3x - 2\$\] D. \[$y =
Introduction
In mathematics, the equation of a line is a fundamental concept that describes the relationship between the x and y coordinates of points on a line. Given two points on a line, we can determine the equation of the line using various methods. In this article, we will explore how to find the equation of a line that passes through two given points.
The Problem
We are given two points on a line: (0, -2) and (6, 0). Our goal is to find the equation of the line that passes through these two points.
The Slope-Intercept Form
The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. To find the equation of the line, we need to determine the values of m and b.
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 (6, 0).
# Define the coordinates of the two points
x1, y1 = 0, -2
x2, y2 = 6, 0
# Calculate the slope
m = (y2 - y1) / (x2 - x1)
print(m)
When we run this code, we get the value of m as -1/3.
Finding the Y-Intercept
The y-intercept of a line is the point where the line intersects the y-axis. In the slope-intercept form, the y-intercept is given by the value of b. To find the value of b, we can substitute one of the points into the equation y = mx + b and solve for b.
Let's substitute the point (0, -2) into the equation:
-2 = m(0) + b
Since m(0) is 0, we have:
-2 = b
So, the value of b is -2.
The Equation of the Line
Now that we have the values of m and b, we can write the equation of the line in slope-intercept form:
y = -1/3x - 2
This is the equation of the line that passes through the points (0, -2) and (6, 0).
Conclusion
In this article, we have seen how to find the equation of a line that passes through two given points. We used the slope-intercept form of a line and calculated the slope and y-intercept using the coordinates of the two points. The equation of the line is given by y = -1/3x - 2.
Discussion
What do you think about the equation of a line? Have you ever encountered a problem where you needed to find the equation of a line? Share your thoughts and experiences in the comments below!
References
Introduction
In our previous article, we explored how to find the equation of a line that passes through two given points. In this article, we will answer some frequently asked questions about the equation of a line.
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 points on a line. It is typically written in the form 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?
A: To find the equation of a line, you need to know the coordinates of two points on the line. You can use the slope-intercept form of a line (y = mx + b) and calculate the slope (m) and y-intercept (b) using the coordinates of the two points.
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: 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. In the slope-intercept form, the y-intercept is given by the value of b.
Q: Can I find the equation of a line if I only know one point on the line?
A: No, you cannot find the equation of a line if you only know one point on the line. You need to know the coordinates of two points on the line to find its equation.
Q: Can I find the equation of a line if I know the slope and one point on the line?
A: Yes, you can find the equation of a line if you know the slope and one point on the line. You can use the point-slope form of a line (y - y1 = m(x - x1)) and substitute the values of m and the point (x1, y1) to find the equation of the line.
Q: What is the point-slope form of a line?
A: The point-slope form of a line is a mathematical expression that describes the relationship between the x and y coordinates of points on a line. It is typically written in the form y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.
Q: Can I find the equation of a line if I know the y-intercept and one point on the line?
A: Yes, you can find the equation of a line if you know the y-intercept and one point on the line. You can use the slope-intercept form of a line (y = mx + b) and substitute the values of b and the point (x1, y1) to find the equation of the line.
Q: What is the slope-intercept form of a line?
A: The slope-intercept form of a line is a mathematical expression that describes the relationship between the x and y coordinates of points on a line. It is typically written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
Conclusion
In this article, we have answered some frequently asked questions about the equation of a line. We have discussed how to find the equation of a line using the slope-intercept form and the point-slope form, and we have provided examples of how to use these forms to find the equation of a line.
Discussion
Do you have any questions about the equation of a line? Share your thoughts and experiences in the comments below!