Find The Graph Of This Linear Equation.${ Y = -\frac{7}{9}x - 5 }$Click On The Correct Answer:- Graph 1- Graph 2- Graph 3- Graph 4
Introduction
Linear equations are a fundamental concept in mathematics, and understanding how to find their graphs is crucial for solving various problems in algebra, geometry, and other branches of mathematics. In this article, we will focus on finding the graph of a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.
What is a Linear Equation?
A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form of y = mx + b, where m and b are constants. The graph of a linear equation is a straight line, and it can be represented on a coordinate plane.
The General Form of a Linear Equation
The general form of a linear equation is y = mx + b, where:
- m is the slope of the line, which represents the rate of change of the line.
- b is the y-intercept of the line, which represents the point where the line intersects the y-axis.
Finding the Graph of a Linear Equation
To find the graph of a linear equation, we need to determine the slope (m) and the y-intercept (b) of the line. Once we have these values, we can plot the line on a coordinate plane.
Step 1: Determine the Slope (m)
The slope of a line can be determined using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
Step 2: Determine the Y-Intercept (b)
The y-intercept of a line is the point where the line intersects the y-axis. It can be determined by substituting x = 0 into the equation and solving for y.
Example: Finding the Graph of a Linear Equation
Let's consider the linear equation y = -7/9x - 5. To find the graph of this equation, we need to determine the slope (m) and the y-intercept (b) of the line.
Step 1: Determine the Slope (m)
Using the formula m = (y2 - y1) / (x2 - x1), we can determine the slope of the line. However, since we are given the equation in the form of y = mx + b, we can directly read the slope from the equation. In this case, the slope is -7/9.
Step 2: Determine the Y-Intercept (b)
To determine the y-intercept, we substitute x = 0 into the equation and solve for y.
y = -7/9(0) - 5 y = -5
Therefore, the y-intercept of the line is -5.
Plotting the Line
Now that we have determined the slope (m) and the y-intercept (b) of the line, we can plot the line on a coordinate plane. The line will pass through the point (0, -5) and will have a slope of -7/9.
Graph Options
Based on the equation y = -7/9x - 5, we can plot the line on a coordinate plane. The correct graph of the equation is:
Graph 1
This graph represents a line with a slope of -7/9 and a y-intercept of -5.
Graph 2
This graph represents a line with a slope of 7/9 and a y-intercept of -5.
Graph 3
This graph represents a line with a slope of -7/9 and a y-intercept of 5.
Graph 4
This graph represents a line with a slope of 7/9 and a y-intercept of 5.
Conclusion
In this article, we have discussed how to find the graph of a linear equation in the form of y = mx + b. We have also provided an example of how to determine the slope (m) and the y-intercept (b) of a line using the equation y = -7/9x - 5. By following these steps, we can plot the line on a coordinate plane and determine the correct graph of the equation.
Final Answer
The correct graph of the equation y = -7/9x - 5 is:
Graph 1
Introduction
Linear equations are a fundamental concept in mathematics, and understanding how to solve them is crucial for success in algebra, geometry, and other branches of mathematics. In this article, we will provide a Q&A guide to help you understand how to solve linear equations and find their graphs.
Q: What is a linear equation?
A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form of y = mx + b, where m and b are constants.
Q: What is the general form of a linear equation?
A: The general form of a linear equation is y = mx + b, where:
- m is the slope of the line, which represents the rate of change of the line.
- b is the y-intercept of the line, which represents the point where the line intersects the y-axis.
Q: How do I find the graph of a linear equation?
A: To find the graph of a linear equation, you need to determine the slope (m) and the y-intercept (b) of the line. Once you have these values, you can plot the line on a coordinate plane.
Q: How do I determine the slope (m) of a line?
A: The slope of a line can be determined using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
Q: How do I determine the y-intercept (b) of a line?
A: The y-intercept of a line is the point where the line intersects the y-axis. It can be determined by substituting x = 0 into the equation and solving for y.
Q: What is the equation y = -7/9x - 5?
A: The equation y = -7/9x - 5 is a linear equation in the form of y = mx + b, where m = -7/9 and b = -5.
Q: What is the slope (m) of the line y = -7/9x - 5?
A: The slope of the line y = -7/9x - 5 is -7/9.
Q: What is the y-intercept (b) of the line y = -7/9x - 5?
A: The y-intercept of the line y = -7/9x - 5 is -5.
Q: What is the graph of the equation y = -7/9x - 5?
A: The graph of the equation y = -7/9x - 5 is a line with a slope of -7/9 and a y-intercept of -5.
Q: How do I plot the line y = -7/9x - 5 on a coordinate plane?
A: To plot the line y = -7/9x - 5 on a coordinate plane, you need to determine the x and y coordinates of the line. The x-coordinate is 0, and the y-coordinate is -5. The line will pass through the point (0, -5) and will have a slope of -7/9.
Q: What are the possible graphs of the equation y = -7/9x - 5?
A: The possible graphs of the equation y = -7/9x - 5 are:
Graph 1
This graph represents a line with a slope of -7/9 and a y-intercept of -5.
Graph 2
This graph represents a line with a slope of 7/9 and a y-intercept of -5.
Graph 3
This graph represents a line with a slope of -7/9 and a y-intercept of 5.
Graph 4
This graph represents a line with a slope of 7/9 and a y-intercept of 5.
Conclusion
In this article, we have provided a Q&A guide to help you understand how to solve linear equations and find their graphs. We have also provided an example of how to determine the slope (m) and the y-intercept (b) of a line using the equation y = -7/9x - 5. By following these steps, you can plot the line on a coordinate plane and determine the correct graph of the equation.
Final Answer
The correct graph of the equation y = -7/9x - 5 is:
Graph 1
This graph represents a line with a slope of -7/9 and a y-intercept of -5.