Which Is The Graph Of The Equation?
In mathematics, a graph of an equation is a set of points that satisfy the equation. The graph of an equation can be used to visualize the relationship between the two variables in the equation.
To find the graph of an equation, we can use the following steps:
- Solve the equation for y in terms of x. This will give us an expression for y in terms of x.
- Choose a few values for x and substitute them into the expression for y. This will give us a set of ordered pairs that satisfy the equation.
- Plot the ordered pairs on a coordinate plane. The points that we plot will be the graph of the equation.
For example, consider the equation y = x. This equation is already solved for y in terms of x. We can choose any values for x, such as 0, 1, 2, and 3. Substituting these values into the equation gives us the following ordered pairs:
(x, y) = (0, 0) (x, y) = (1, 1) (x, y) = (2, 2) (x, y) = (3, 3) Plotting these ordered pairs on a coordinate plane gives us the following graph:
[Image of a straight line with a slope of 1 and a y-intercept of 0]As you can see, the graph of the equation y = x is a straight line with a slope of 1 and a y-intercept of 0.
Here are some additional questions that you can ask to help you determine which graph is the graph of an equation:
- Does the graph pass through the origin (0, 0)? If so, the equation has a y-intercept of 0.
- Does the graph have a positive or negative slope? The slope of the graph can be determined by finding the change in y divided by the change in x for two points on the graph. If the slope is positive, the graph will rise as x increases. If the slope is negative, the graph will fall as x increases.
- Does the graph have a point of intersection with the x-axis? If so, the equation has a solution for x = 0.
By answering these questions, you can often determine which graph is the graph of an equation.
Here are some additional examples of equations and their graphs:
- Equation: y = 2x – 3
- Graph: A line with a slope of 2 and a y-intercept of -3
- Equation: y = x^2
- Graph: A parabola that opens upward
- Equation: y = e^x
- Graph: An exponential function
By understanding how to graph equations, you can gain a better understanding of the relationships between variables.
