Write a sentence comparing the graphs of equations with a positive coefficient of x and graphs with a negeative coefficient of x
When comparing the graphs of equations with a positive coefficient of x and graphs with a negative coefficient of x, you will notice that the positive coefficient causes the graph to slope upwards from left to right, while the negative coefficient causes the graph to slope downwards.
To understand this concept and visualize it, you can follow these steps:
1. Identify the equation you want to graph. For example, let's consider the equation y = 2x and y = -2x.
2. Plot points on a coordinate system. To do this, select different values of x (e.g., -3, -2, -1, 0, 1, 2, 3) substitute them into the equation, and calculate the corresponding y-values.
For y = 2x:
- When x = -3, y = -6 ((-3) * 2 = -6)
- When x = -2, y = -4 ((-2) * 2 = -4)
- When x = -1, y = -2 ((-1) * 2 = -2)
- When x = 0, y = 0 ((0) * 2 = 0)
- When x = 1, y = 2 ((1) * 2 = 2)
- When x = 2, y = 4 ((2) * 2 = 4)
- When x = 3, y = 6 ((3) * 2 = 6)
For y = -2x:
- When x = -3, y = 6 ((-3) * (-2) = 6)
- When x = -2, y = 4 ((-2) * (-2) = 4)
- When x = -1, y = 2 ((-1) * (-2) = 2)
- When x = 0, y = 0 ((0) * (-2) = 0)
- When x = 1, y = -2 ((1) * (-2) = -2)
- When x = 2, y = -4 ((2) * (-2) = -4)
- When x = 3, y = -6 ((3) * (-2) = -6)
3. Plot the points on the coordinate plane. Connect the dots to form a straight line for each equation.
With these steps, you will have two graphs, one with a positive coefficient of x and the other with a negative coefficient of x. Comparing them visually, you will observe the difference in the slopes and how one slopes upward while the other slopes downward.