two ways to determine if an equation is linear

1. The calculated slope is the same at all points.

2. A graph of the Eq is a st. line.

What are two ways to determine if a relationship is linear

There are two ways to determine if an equation is linear:

1. Degree of the equation: A linear equation is a polynomial equation with a degree of 1. This means that the highest power of the variable in the equation is 1. For example, equations like y = 3x + 2 or 2x - 5y = 8 are linear because the variables x and y are raised to the power of 1.

2. Linearity in variables: A linear equation has variables that are only multiplied by a constant and added or subtracted. In other words, each variable appears with a degree of 1 and is not raised to any power, multiplied together, or divided. For example, equations like 4x - 2y = 6 or x + 2y - z = 3 are linear because the variables appear with a degree of 1 and are not multiplied together or divided.

If an equation satisfies both of these conditions, it can be determined as a linear equation.

To determine if an equation is linear, you can use the following two ways:

1. Check the Degree of the Equation:
The degree of an equation refers to the highest power of the variable(s) present in the equation. In a linear equation, the highest power of the variables should be 1. To determine this, look for the exponent of the variable(s) in the equation. If the exponent is 1, then the equation is linear. If the exponent is greater than 1 or there are variables with different exponents, then the equation is not linear.

For example:
- "3x + 2y = 7" is a linear equation because both x and y have an exponent of 1.
- "5x^2 + 2y = 8" is not a linear equation because x has an exponent of 2.

2. Check for Linearity in Variables:
Linear equations involve variables in a linear relationship, meaning they appear only with a power of 1 and are not multiplied or divided by other variables. In a linear equation, the variables should be present in a simple linear form without any complex operations. If the variables are multiplied or divided, or if non-linear functions like square roots or trigonometric functions are involved, the equation is not linear.

For example:
- "2x + 3y = 4" is a linear equation as both variables appear in a simple linear form, added together.
- "5x * y = 10" is not a linear equation because the variables x and y are multiplied together.

By applying these two methods, you can determine if an equation is linear or not.