Question

How do you describe a linear equation?

a. An equation that forms a straight line when graphed.
b. An equation that contains variables with a maximum degree of 1.
c. An equation that represents a linear relationship between two or more variables.
d. All of the above.

Answer 1

A linear equation describes a direct relationship between two variables that forms a straight line when graphed and contains variables of the highest degree of 1, typically in the form y = mx + b, with m representing the slope and b the y-intercept.

Step-by-step explanation:

A linear equation can be described as an equation that satisfies all of the following criteria:

• (a) It forms a straight line when graphed on a coordinate plane.
• (b) Contains variables of which the highest power (degree) is 1.
• (c) Represents a linear relationship between two or more variables.
• (d) Therefore, the correct answer is 'All of the above'.

Essentially, a linear equation is typically written in the form y = mx + b, where m is the slope of the line and b is the y-intercept, indicating the point where the line crosses the y-axis. In a linear equation, the slope 'm' quantifies the rate of change between the dependent and independent variables while the 'y-intercept' represents the y-coordinate of the point where the line intersects the y-axis when x equals 0.