-y%3D-4x%2B2.jpeg "(-2 5) Y=-4x+2")
Understanding the Equation: y = -4x + 2
This equation represents a linear relationship between two variables, x and y.
Here's a breakdown:
- y = -4x + 2 is in slope-intercept form, which is y = mx + b.
- m represents the slope of the line. In this case, the slope is -4. This means that for every 1 unit increase in x, y decreases by 4 units.
- b represents the y-intercept, the point where the line crosses the y-axis. Here, the y-intercept is 2. This means the line passes through the point (0, 2).
Visualizing the Equation
To visualize this equation, imagine a graph with x and y axes.
- Plot the y-intercept: Start by placing a point at (0, 2).
- Use the slope to find other points: Since the slope is -4, move down 4 units and right 1 unit from the y-intercept. This will give you another point on the line. You can repeat this process to find as many points as you need.
- Draw the line: Connect the points you've plotted to create a straight line.
Understanding (-2, 5)
The point (-2, 5) signifies a specific point on the x-y plane.
- x = -2 indicates that the point is located 2 units to the left of the y-axis.
- y = 5 indicates that the point is located 5 units above the x-axis.
To determine if the point (-2, 5) lies on the line represented by the equation y = -4x + 2, substitute the x and y values into the equation:
- y = -4x + 2
- 5 = -4(-2) + 2
- 5 = 8 + 2
- 5 ≠ 10
Therefore, the point (-2, 5) does not lie on the line represented by the equation y = -4x + 2.