Which Equation Is Represented By The Graph Below?
In mathematics, an equation is a statement that two expressions are equal. The graph of an equation is a set of points that satisfy the equation. To determine which equation is represented by a graph, we can look for the features of the graph that are consistent with the properties of the equation.
Features of Graphs
Some of the features of graphs that we can look for include:
- The shape of the graph: Some equations, such as linear equations, have graphs that are straight lines. Others, such as quadratic equations, have graphs that are parabolas.
- The slope of the graph: The slope of a line is a measure of how steep the line is. We can find the slope of a line by using the rise over run method.
- The y-intercept of the graph: The y-intercept of a line is the point where the line crosses the y-axis.
- The zeros of the graph: The zeros of a graph are the points where the graph crosses the x-axis.
Examples
Let’s look at some examples of how we can use these features to determine which equation is represented by a graph.
Example 1
The graph below is a straight line. The slope of the line is 2. The y-intercept of the line is 4.
[Image of a straight line with a slope of 2 and a y-intercept of 4]Which equation is represented by this graph?
Possible answers:
- y = 2x + 4
- y = 2x – 4
- y = -2x + 4
- y = -2x – 4
The correct answer is y = 2x + 4. This is because the slope of the line is 2, which is the same as the coefficient of x in the equation y = 2x + 4. The y-intercept of the line is also 4, which is the same as the constant term in the equation.
Example 2
The graph below is a parabola. The vertex of the parabola is at (0, 2).
[Image of a parabola with a vertex at (0, 2)]Which equation is represented by this graph?
Possible answers:
- y = x^2 + 2
- y = x^2 – 2
- y = -x^2 + 2
- y = -x^2 – 2
The correct answer is y = x^2 + 2. This is because the vertex of the parabola is at (0, 2), which is the same as the value of y when x is 0 in the equation y = x^2 + 2.
Questions
Here are some questions that you can ask yourself to help you determine which equation is represented by a graph:
- What is the shape of the graph?
- What is the slope of the graph?
- What is the y-intercept of the graph?
- What are the zeros of the graph?
By answering these questions, you can narrow down the possible equations that could represent the graph.
