Final answer:
The equation y = -2x is a linear equation because it is in the form y = a + bx, with a slope of -2 and a y-intercept of 0. It will graph as a straight line.
Step-by-step explanation:
When examining the equation y = -2x, it's important to recognize whether it is linear or nonlinear. A linear equation in two variables typically takes the form y = a + bx, where a represents the y-intercept (the value of y when x is zero) and b represents the slope (the rate at which y changes with respect to x). Since -2 is the coefficient of x (representing the slope) and there is no other term in the equation, it matches the general form of a linear equation with a y-intercept of 0 and a slope of -2.
In the context of commonly used relationships in various courses, expressing equations graphically is a significant aspect, and the graph of any linear equation, including y = -2x, would be a straight line. Therefore, y = -2x is indeed a linear equation because it follows the specified format and would produce a straight line when graphed on a coordinate plane.