-2y%3D4x-6.jpeg "(-2 5) 2y=4x-6")
Understanding the Equation: (-2, 5) 2y = 4x - 6
This equation presents a bit of a puzzle! Let's break it down:
1. The Point (-2, 5): This point tells us a crucial piece of information: the line represented by the equation passes through the point (-2, 5). This means if we substitute x = -2 and y = 5 into the equation, it should hold true.
2. The Equation: 2y = 4x - 6: This is the standard form of a linear equation.
- 2y: The left side of the equation represents the y-values of the line.
- 4x - 6: The right side of the equation represents the x-values of the line.
Putting it Together:
The combination of the point (-2, 5) and the equation 2y = 4x - 6 essentially defines a line. We can use this information to:
- Find the Slope: We can manipulate the equation into slope-intercept form (y = mx + b), where 'm' is the slope and 'b' is the y-intercept.
- Graph the Line: We can use the point (-2, 5) and the slope to plot the line on a coordinate plane.
Important Note: The equation is written with "2y = 4x - 6". This suggests a simplification or transformation might have occurred. It's important to note that if the original equation was different, the solution may differ.
Let's explore some possible scenarios and solutions:
Scenario 1: The Equation is Already Simplified
- If the given equation is the simplified form, we can find the slope and y-intercept directly:
- Divide both sides of the equation by 2: y = 2x - 3
- Now, we see that the slope (m) is 2 and the y-intercept (b) is -3.
Scenario 2: The Equation Has a Constant Multiplier
- If there was a constant multiplier on the left side of the equation, we can find it by substituting the point (-2, 5):
- Substitute x = -2 and y = 5 into the equation: 2 * 5 = 4 * (-2) - 6
- Simplify: 10 = -14, which is not true. This suggests the original equation might have a constant multiplier on the left side.
- We can explore values for the constant multiplier that would make the equation hold true for the point (-2, 5).
Solving for the Constant Multiplier:
- Let's assume the original equation was k * 2y = 4x - 6.
- Substitute x = -2 and y = 5: k * 2 * 5 = 4 * (-2) - 6
- Simplify: 10k = -14
- Solve for k: k = -14/10 = -7/5
In conclusion:
The equation (-2, 5) 2y = 4x - 6 provides information about a line that passes through the point (-2, 5). The exact form of the equation depends on whether it's simplified or has a constant multiplier. We can utilize the given information to determine the slope, y-intercept, and graph the line.