What is a linear equation?

What is a linear equation?

• A. A diagram of a geometric shape
• B. A mathematical statement that shows the relationship between two variables, typically in the form of y = mx + b
• C. A statistical test for correlation
• D. A method for calculating compound interest

Answer: (B)

A linear equation describes a relationship between two variables that changes at a constant rate. It’s usually written as y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope (how much y changes when x increases by 1), and b is the y-intercept (the value of y when x is 0). Graphically, this relationship forms a straight line, which is the hallmark of linear equations. This form specifically captures a steady rate of change, unlike the other options. A diagram of a geometric shape is just a picture, not an equation. A statistical test for correlation measures how strongly two variables move together, but it isn’t an equation expressing a direct, linear relationship. A method for calculating compound interest involves growth that is not linear, since it compounds over time. So the description in y = mx + b is the correct way to express a linear equation.

A linear equation describes a relationship between two variables that changes at a constant rate. It’s usually written as y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope (how much y changes when x increases by 1), and b is the y-intercept (the value of y when x is 0). Graphically, this relationship forms a straight line, which is the hallmark of linear equations.

This form specifically captures a steady rate of change, unlike the other options. A diagram of a geometric shape is just a picture, not an equation. A statistical test for correlation measures how strongly two variables move together, but it isn’t an equation expressing a direct, linear relationship. A method for calculating compound interest involves growth that is not linear, since it compounds over time. So the description in y = mx + b is the correct way to express a linear equation.