What Is The Slope Of The Line That Goes Through The Points \[$(-2, 5)\$\] And \[$(0, 2)\$\]?Select The Correct Answer:A. \[$m = \frac{2}{3}\$\]B. \[$m = -\frac{2}{3}\$\]C. \[$m = -\frac{3}{2}\$\]D. \[$m =
Introduction
In mathematics, the slope of a line is a measure of how steep it is. It is calculated by finding the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. In this article, we will explore how to find the slope of a line that goes through two given points.
What is the Formula for Slope?
The formula for slope is:
m = (y2 - y1) / (x2 - x1)
where m is the slope, and (x1, y1) and (x2, y2) are the coordinates of the two points on the line.
Example: Finding the Slope of a Line
Let's use the points (-2, 5) and (0, 2) to find the slope of the line that goes through them.
Step 1: Identify the Coordinates of the Two Points
The coordinates of the two points are (-2, 5) and (0, 2).
Step 2: Plug the Coordinates into the Formula for Slope
m = (y2 - y1) / (x2 - x1) m = (2 - 5) / (0 - (-2)) m = (-3) / (2) m = -3/2
Step 3: Simplify the Fraction (Optional)
In this case, the fraction -3/2 is already in its simplest form.
Conclusion
The slope of the line that goes through the points (-2, 5) and (0, 2) is -3/2.
Answer
The correct answer is:
C. m = -3/2
Why is the Slope Important?
The slope of a line is an important concept in mathematics because it helps us understand the relationship between the x and y coordinates of a point on the line. It is used in a variety of applications, including:
- Graphing: The slope of a line is used to determine the steepness of the line and to draw the line on a graph.
- Equations of Lines: The slope of a line is used to write the equation of the line in slope-intercept form (y = mx + b).
- Real-World Applications: The slope of a line is used to model real-world situations, such as the motion of an object or the growth of a population.
Tips and Tricks
- Make sure to plug in the correct coordinates into the formula for slope.
- Simplify the fraction (if necessary).
- Use the slope to determine the steepness of the line.
Common Mistakes
- Forgetting to plug in the correct coordinates into the formula for slope.
- Not simplifying the fraction (if necessary).
- Using the wrong formula for slope.
Conclusion
Q: What is the slope of a line?
A: The slope of a line is a measure of how steep it is. It is calculated by finding the ratio of the vertical change (rise) to the horizontal change (run) between 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 m is the slope, and (x1, y1) and (x2, y2) are the coordinates of the two points on the line.
Q: What is the difference between a positive and negative slope?
A: A positive slope indicates that the line is rising from left to right, while a negative slope indicates that the line is falling from left to right.
Q: Can the slope of a line be zero?
A: Yes, the slope of a line can be zero. This occurs when the line is horizontal, meaning that it does not rise or fall.
Q: Can the slope of a line be undefined?
A: Yes, the slope of a line can be undefined. This occurs when the line is vertical, meaning that it does not have a horizontal change (run).
Q: How do I use the slope to determine the steepness of a line?
A: To determine the steepness of a line, you can use the slope. A steeper line has a larger slope, while a less steep line has a smaller slope.
Q: Can I use the slope to find the equation of a line?
A: Yes, you can use the slope to find the equation of a line. The equation of a line in slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept.
Q: What is the y-intercept?
A: The y-intercept is the point where the line intersects the y-axis. It is the value of y when x is equal to zero.
Q: Can I use the slope to model real-world situations?
A: Yes, you can use the slope to model real-world situations, such as the motion of an object or the growth of a population.
Q: What are some common mistakes to avoid when finding the slope of a line?
A: Some common mistakes to avoid when finding the slope of a line include:
- Forgetting to plug in the correct coordinates into the formula for slope
- Not simplifying the fraction (if necessary)
- Using the wrong formula for slope
Q: How do I know if I have found the correct slope?
A: To know if you have found the correct slope, you can check your work by plugging the slope back into the formula for slope and verifying that it is true.
Conclusion
In conclusion, the slope of a line is an important concept in mathematics that helps us understand the relationship between the x and y coordinates of a point on the line. By following the steps outlined in this article, you can find the slope of a line that goes through two given points.