Have you ever looked at a graph and wondered which equation could represent it? Understanding the relationship between a graph and its equation can be a fascinating exercise in mathematics. In this article, we will delve into the world of algebraic equations and explore three possibilities for the equation that represents the given graph: Y = –3x + 3, Y = 3x – 3, and Y = 3x – Y = –X + 3. By the end, you will have a clear understanding of how to determine which equation matches a graphed function, equipping you with a valuable skill in algebraic analysis.
Before we dive into the intricacies of these equations, let’s explore the graphed function and its potential representations. The graph we are analyzing appears to be a straight line with a negative slope intercepting the y-axis at the point (0, 3). As we examine the given equations, we will closely observe how they align with the key features of this graph. By doing so, we can confidently determine which equation best fits the observed characteristics of the graphed function.
Which Equation Represents The Graphed Function?
1. A straight line passes through the point (0, 3) and has a negative slope.
The given graph is a straight line that passes through the point (0, 3) and has a negative slope. To determine which equation represents this graph, we need to consider the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Since the given line has a negative slope, we know that its equation will have a negative coefficient of x. Looking at the options, we can see that y = -3x + 3 is the only equation with a negative coefficient of x, which matches the given graph. Therefore, the equation y = -3x + 3 represents the graphed function.
2. A straight line passes through the point (0, -3) and has a positive slope.
The graph provided shows a straight line that passes through the point (0, -3) and has a positive slope. To determine which equation represents this graph, let’s analyze the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
Since the line has a positive slope, we know that its equation will have a positive coefficient of x. Analyzing the given equations, we can see that y = 3x – 3 is the only option with a positive coefficient of x, which matches the given graph. Thus, the equation y = 3x – 3 represents the graphed function.
3. A straight line passes through the point (0, 3) and is parallel to the x-axis.
The graph provided represents a straight line that passes through the point (0, 3) and is parallel to the x-axis. To identify which equation represents this graph, let’s examine the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
Considering that the line is parallel to the x-axis, we know its slope is 0. Out of the given equations, only y = 3 fits the criteria since it does not have an x term, indicating a slope of 0. Hence, the equation y = 3 represents the graphed function.
4. A straight line passes through the point (0, -3) and is parallel to the y-axis.
The given graph shows a straight line that passes through the point (0, -3) and is parallel to the y-axis. To determine which equation represents this graph, we need to analyze the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
Since the line is parallel to the y-axis, its slope is undefined. Looking at the available equations, none of them include an undefined slope. Therefore, none of the given equations represent the graphed function.
5. A straight line passes through the point (0, 3) and has a positive slope equal to 1.
The provided graph depicts a straight line passing through the point (0, 3) with a positive slope of 1. To identify which equation represents this graph, let’s examine the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
Analyzing the given equations, we can see that y = x + 3 is the only equation with a slope equal to 1, which matches the given graph. Therefore, the equation y = x + 3 represents the graphed function.
6. A straight line passes through the point (0, -3) and has a negative slope equal to 1.
The graph provided shows a straight line passing through the point (0, -3) with a negative slope equal to 1. To determine which equation represents this graph, we need to consider the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
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Reviewing the given equations, we can see that the equation y = -x – 3 is the only option with a negative slope equal to 1, which matches the provided graph. Thus, the equation y = -x – 3 represents the graphed function.
7. A straight line passes through the point (0, 3) and has a slope equal to -1.
The given graph represents a straight line passing through the point (0, 3) with a slope equal to -1. To determine which equation represents this graph, let’s examine the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
Examining the given equations, we can see that y = -x + 3 is the only equation with a slope equal to -1, matching the provided graph. Hence, the equation y = -x + 3 represents the graphed function.
8. A straight line passes through the point (0, -3) and is perpendicular to the x-axis.
The graph provided shows a straight line that passes through the point (0, -3) and is perpendicular to the x-axis. To determine which equation represents this graph, we need to analyze the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
Considering the line is perpendicular to the x-axis, its slope is undefined. None of the given equations have an undefined slope, indicating that none of the provided equations represent the graphed function.
9. A straight line passes through the point (0, 3) and is perpendicular to the y-axis.
The given graph illustrates a straight line passing through the point (0, 3) and is perpendicular to the y-axis. To identify which equation represents this graph, let’s examine the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
Since the line is perpendicular to the y-axis, its slope is 0. Looking at the available equations, only y = 3 fits the criteria since it does not have an x term, indicating a slope of 0. Therefore, the equation y = 3 represents the graphed function.
10. A straight line passes through the point (0, -3) and has a slope equal to 3.
The provided graph depicts a straight line passing through the point (0, -3) with a slope equal to 3. To determine which equation represents this graph, let’s analyze the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
Analyzing the given equations, we can see that the equation y = 3x – 3 is the only option with a slope equal to 3, matching the provided graph. Thus, the equation y = 3x – 3 represents the graphed function.
Determining the Equation Representing the Graphed Function
1. Start by examining the given graph that represents a linear function.
2. Identify the slope of the line by observing its steepness. Remember that slope (m) represents the rate of change of the function.
3. Determine whether the line intercepts the y-axis or the x-axis. The value where the line intercepts the y-axis is the y-intercept (b).
4. Write down the slope-intercept form of the equation: y = mx + b, where m represents the slope and b represents the y-intercept.
5. Compare the given options: Y = –3x + 3, Y = 3x – 3, and Y = 3x – Y = –X + 3 with the slope-intercept form and determine the correct equation.
6. Substitute the identified values of slope and y-intercept into each equation option and see which option accurately represents the given graph.
7. The equation that matches the graphed function is the correct answer.
FAQ: Which Equation Represents The Graphed Function?
1. Which equation represents the graphed function?
The equation Y = –3x + 3 represents the graphed function.
2. What is the equation of the graphed function?
The equation of the graphed function is Y = –3x + 3.
3. What is the slope of the graphed function?
The slope of the graphed function is -3.
4. What is the y-intercept of the graphed function?
The y-intercept of the graphed function is 3.
5. How can I represent the graphed function using slope-intercept form?
The graphed function can be represented using slope-intercept form as Y = mx + b, where m represents the slope (-3) and b represents the y-intercept (3).
Conclusion
After analyzing the graph, we find that the equation Y = –3x + 3 represents the graphed function. The slope of the function is -3 and the y-intercept is 3. The function can be represented in slope-intercept form as Y = mx + b.