Which Graph Matches the Equation?
In mathematics, a linear equation is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The graph of a linear equation is a straight line.
To determine which graph matches a given linear equation, we can use the following steps:
- Find the slope of the line. The slope of a line is equal to the change in y divided by the change in x. For example, the slope of the line y = 2x + 1 is equal to 2.
- Find the y-intercept of the line. The y-intercept of a line is the point where the line crosses the y-axis. For example, the y-intercept of the line y = 2x + 1 is equal to 1.
- Plot the points that satisfy the equation. To do this, we can choose any value for x and then solve for y. For example, if we set x = 0, then we get y = b = 1. This point is the y-intercept of the line. We can then choose another value for x, such as x = 1. This gives us y = 2(1) + 1 = 3. We can then plot this point on the graph.
Once we have plotted enough points, we can draw a straight line through those points. This line will be the graph of the given linear equation.
Examples
Let’s consider the following linear equations:
- y = 2x + 1
- y = -x – 1
- y = 1/2x – 1
To determine which graph matches each equation, we can follow the steps above.
For the equation y = 2x + 1, the slope is 2 and the y-intercept is 1. Plotting the points (0, 1) and (1, 3) gives us the following graph:
[Image of a straight line with a slope of 2 and a y-intercept of 1]For the equation y = -x – 1, the slope is -1 and the y-intercept is -1. Plotting the points (0, -1) and (1, -2) gives us the following graph:
[Image of a straight line with a slope of -1 and a y-intercept of -1]For the equation y = 1/2x – 1, the slope is 1/2 and the y-intercept is -1. Plotting the points (0, -1) and (1, -0.5) gives us the following graph:
[Image of a straight line with a slope of 1/2 and a y-intercept of -1]Questions
Here are some questions that you can ask yourself to help you determine which graph matches a given linear equation:
- What is the slope of the line?
- What is the y-intercept of the line?
- What points satisfy the equation?
Once you have answered these questions, you should be able to identify the correct graph.
Here are some examples of questions that you can ask:
- Which graph has a slope of 2?
- Which graph has a y-intercept of 5?
- Which graph passes through the points (0, 1) and (1, 3)?
By answering these questions, you can quickly and easily identify the correct graph.