The equation x + y = -4 is a linear equation because it can be rearranged to the standard form y = -x - 4, displaying a direct relationship between x and y that graphs as a straight line, with a slope of -1 and a y-intercept of -4.
Yes, x + y = -4 is indeed a linear equation. Linear equations are generally of the form y = a + bx, where a is the y-intercept, b represents the slope, x is the independent variable, and y is the dependent variable.
In the given equation, if we solve for y, we get y = -x - 4. Here, -1 is the coefficient of x (the slope), and -4 is the y-intercept.
A linear equation graphs as a straight line on a coordinate plane. Regardless of the values of x, the graph of this equation will always be a straight line, which is a key characteristic of linear equations.
For instance, equations such as 7y = 6x + 8, 4y = 8, and y + 7 = 3x are also linear equations and will graph as straight lines as well. Examples of linear equations provided include a variety of slopes and intercepts, reinforcing the concept that a linear equation can take many forms but always represents a straight line graphically.
The straightforward structure of these equations makes them fundamental in mathematics, reflecting relationships where one variable changes at a constant rate with respect to another.