Line GH Contains Points G(-2, 6) And H(5, -3). What Is The Slope Of Line GH?A. 3 B. 0 C. -11/9 D. 37/58
Understanding the Concept of Slope
In mathematics, the slope of a line is a measure of how steep it is. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. The slope is often denoted by the letter 'm' and is a fundamental concept in geometry and algebra.
The Formula for Slope
The formula for calculating the slope of a line is:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Applying the Formula to Line GH
Given the coordinates of points G(-2, 6) and H(5, -3), we can apply the formula to calculate the slope of line GH.
Step 1: Identify the Coordinates
The coordinates of points G and H are:
G(-2, 6) H(5, -3)
Step 2: Plug in the Values
Using the formula, we can plug in the values as follows:
m = (-3 - 6) / (5 - (-2)) m = (-9) / (7)
Step 3: Simplify the Fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 1.
m = -9 / 7
Step 4: Write the Answer in the Required Format
The slope of line GH is -9/7, which can be written as a fraction or a decimal. In this case, we will leave it as a fraction.
Conclusion
In conclusion, the slope of line GH is -9/7. This can be calculated using the formula for slope, which is m = (y2 - y1) / (x2 - x1). By plugging in the coordinates of points G and H, we can determine the slope of the line.
Answer
The correct answer is C. -11/9 is incorrect, the correct answer is -9/7 but it is not in the options, the closest answer is C. -11/9 but it is not correct.
Why is -11/9 not the correct answer?
-11/9 is not the correct answer because it is not the result of the calculation. When we plug in the values into the formula, we get -9/7, not -11/9.
Why is -9/7 not in the options?
-9/7 is not in the options because the question asks for the slope of line GH, and the options are A. 3, B. 0, C. -11/9, and D. 37/58. However, the correct answer is -9/7, which is not among the options.
What is the closest answer?
The closest answer is C. -11/9, but it is not the correct answer. The correct answer is -9/7, which is not among the options.
Why is 37/58 not the correct answer?
37/58 is not the correct answer because it is not the result of the calculation. When we plug in the values into the formula, we get -9/7, not 37/58.
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 as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.
Q: How is the slope of a line calculated?
A: The slope of a line is calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of 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: What is the slope of a horizontal line?
A: The slope of a horizontal line is 0, since there is no vertical change (rise) between any two points on the line.
Q: What is the slope of a vertical line?
A: The slope of a vertical line is undefined, since there is no horizontal change (run) between any two points on the line.
Q: Can the slope of a line be zero?
A: Yes, the slope of a line can be zero, which indicates that the line is horizontal.
Q: Can the slope of a line be undefined?
A: Yes, the slope of a line can be undefined, which indicates that the line is vertical.
Q: How is the slope of a line used in real-world applications?
A: The slope of a line is used in a variety of real-world applications, including:
- Calculating the steepness of a roof or a hill
- Determining the rate of change of a quantity over time
- Finding the equation of a line that passes through two points
- Calculating the distance between two points on a line
Q: What is the significance of the slope-intercept form of a line?
A: The slope-intercept form of a line, y = mx + b, is significant because it allows us to easily identify the slope (m) and the y-intercept (b) of a line.
Q: Can the slope of a line be a fraction?
A: Yes, the slope of a line can be a fraction, which indicates that the line is not a simple horizontal or vertical line.
Q: Can the slope of a line be a decimal?
A: Yes, the slope of a line can be a decimal, which indicates that the line is not a simple horizontal or vertical line.
Q: How is the slope of a line used in engineering and architecture?
A: The slope of a line is used in engineering and architecture to calculate the steepness of roofs, hills, and other structures, as well as to determine the rate of change of quantities over time.
Q: Can the slope of a line be used to calculate the distance between two points?
A: Yes, the slope of a line can be used to calculate the distance between two points, by using the formula:
d = |(y2 - y1) / (x2 - x1)|
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Q: What is the relationship between the slope of a line and its equation?
A: The slope of a line is related to its equation by the formula:
y = mx + b
where m is the slope and b is the y-intercept.
Q: Can the slope of a line be used to determine the equation of a line?
A: Yes, the slope of a line can be used to determine the equation of a line, by using the formula:
y = mx + b
where m is the slope and b is the y-intercept.
Q: What is the significance of the slope of a line in physics and engineering?
A: The slope of a line is significant in physics and engineering because it is used to calculate the rate of change of quantities over time, such as velocity and acceleration.
Q: Can the slope of a line be used to calculate the velocity of an object?
A: Yes, the slope of a line can be used to calculate the velocity of an object, by using the formula:
v = m * t
where v is the velocity, m is the slope, and t is time.
Q: What is the relationship between the slope of a line and its graph?
A: The slope of a line is related to its graph by the fact that the slope is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
Q: Can the slope of a line be used to determine the graph of a line?
A: Yes, the slope of a line can be used to determine the graph of a line, by using the formula:
y = mx + b
where m is the slope and b is the y-intercept.
Q: What is the significance of the slope of a line in economics and finance?
A: The slope of a line is significant in economics and finance because it is used to calculate the rate of change of quantities over time, such as the rate of inflation or the rate of return on investment.
Q: Can the slope of a line be used to calculate the rate of inflation?
A: Yes, the slope of a line can be used to calculate the rate of inflation, by using the formula:
r = m * t
where r is the rate of inflation, m is the slope, and t is time.
Q: What is the relationship between the slope of a line and its equation in three dimensions?
A: The slope of a line in three dimensions is related to its equation by the formula:
r = m * t
where r is the position vector, m is the slope, and t is time.
Q: Can the slope of a line be used to determine the equation of a line in three dimensions?
A: Yes, the slope of a line can be used to determine the equation of a line in three dimensions, by using the formula:
r = m * t
where r is the position vector, m is the slope, and t is time.
Q: What is the significance of the slope of a line in computer science and programming?
A: The slope of a line is significant in computer science and programming because it is used to calculate the rate of change of quantities over time, such as the rate of change of a variable or the rate of change of a function.
Q: Can the slope of a line be used to calculate the rate of change of a variable?
A: Yes, the slope of a line can be used to calculate the rate of change of a variable, by using the formula:
r = m * t
where r is the rate of change, m is the slope, and t is time.
Q: What is the relationship between the slope of a line and its graph in polar coordinates?
A: The slope of a line in polar coordinates is related to its graph by the fact that the slope is the ratio of the radial change (rise) to the angular change (run) between any two points on the line.
Q: Can the slope of a line be used to determine the graph of a line in polar coordinates?
A: Yes, the slope of a line can be used to determine the graph of a line in polar coordinates, by using the formula:
r = m * θ
where r is the radial distance, m is the slope, and θ is the angle.
Q: What is the significance of the slope of a line in statistics and data analysis?
A: The slope of a line is significant in statistics and data analysis because it is used to calculate the rate of change of quantities over time, such as the rate of change of a variable or the rate of change of a function.
Q: Can the slope of a line be used to calculate the rate of change of a variable in statistics?
A: Yes, the slope of a line can be used to calculate the rate of change of a variable in statistics, by using the formula:
r = m * t
where r is the rate of change, m is the slope, and t is time.
Q: What is the relationship between the slope of a line and its equation in parametric form?
A: The slope of a line in parametric form is related to its equation by the fact that the slope is the ratio of the change in the parameter (t) to the change in the dependent variable (y).
Q: Can the slope of a line be used to determine the equation of a line in parametric form?
A: Yes, the slope of a line can be used to determine the equation of a line in parametric form, by using the formula:
y = m * t + b
where y is the dependent variable, m is the slope, t is the parameter, and b is the constant term.
Q: What is the significance of the slope of a line in calculus and differential equations?
A: The slope of a line is significant in calculus and differential equations because it is used to calculate the rate of change of quantities over time, such as the rate of change