Answer:
The equations y = 2x and y = -2x represent two different lines with different slopes and behaviors.
Step-by-step explanation:
The given equation is y = 2x.
This equation represents a linear function, where y is equal to 2 times x. This means that for every value of x, the corresponding value of y will be twice that of x.
For example, if we let x = 1, then y = 2(1) = 2. So, when x is 1, y is 2.
Similarly, if we let x = -3, then y = 2(-3) = -6. So, when x is -3, y is -6.
In general, the equation y = 2x represents a straight line on a graph with a slope of 2 and passing through the origin (0, 0). As x increases, y will also increase, and as x decreases, y will also decrease.
On the other hand, the equation y = -2x represents a linear function with a slope of -2. This means that for every value of x, the corresponding value of y will be negative twice that of x.
For example, if we let x = 2, then y = -2(2) = -4. So, when x is 2, y is -4.
Similarly, if we let x = -4, then y = -2(-4) = 8. So, when x is -4, y is 8.
In general, the equation y = -2x represents a straight line on a graph with a slope of -2 and passing through the origin (0, 0). As x increases, y will decrease, and as x decreases, y will increase.
Therefore, the equations y = 2x and y = -2x represent two different lines with different slopes and behaviors.
