Question

The graph of 2x + 3y + 6 = 0 is a ___________ that is why any first-degree equation in x, y is called _____________.
A) Line, linear equation
B) Equation, line
C) Circle, linear equation
D) None of these

Answer 1

Hint: For solving this question we compare the given equation with the available general equations for two-dimensional figures and analyze it. By using this methodology, we get our answer and type of equation.

Complete step-by-step answer:
A line is uniquely determined by two points, like the line passing through points A and B.

The line with x-intercept b and y-intercept a is given by the intercept form.
$\dfrac{x}{a}+\dfrac{y}{b}=1$
The standard form of the line is: ax + by + c = 0.
According to the problem statement, we are given an equation 2x + 3y + 6 = 0.
From comparing the given equations with the standard form, we get a =2, b = 3, c = 6.
Therefore, it is the equation of a line.

The given equation 2x + 3y + 6 = 0, is the linear equation because each term involved in the linear equation is either a constant or single variable or a product of a constant and variable.
Hence, the graph of 2x + 3y + 6 = 0 is a line that is why any first-degree equation in x, y is called linear equation.
Hence, option (A) is correct.

Note: For solving this problem, the knowledge of general equations in two-dimensional figures is required. Since the degree of the variables involved in the equation is one, so this equation is linear. It is also an alternative method.