How can you tell if an equation of a relation represents a linear relation?
THanks to everyon who helps :)
linear = first degree only, no squares, no cubes, no square roots,no products of variable.
so x+3y=c is a linear equation
x^3+y=c is NOT
-x+12y=45 is linear
1+ xy=c is NOT
thanks so much that helped me a lot !!
To determine if an equation represents a linear relation, you need to check if the equation meets the criteria of a linear equation. Here are the steps to follow:
1. Verify that the equation represents a function: A linear relation must be a function, meaning that for every input (x-value), there is a unique output (y-value). You can determine this by checking if every x-value in the equation corresponds to only one y-value.
2. Find the highest power of the variable: In a linear relation, the highest power of the variable (usually represented by "x") is always 1. If the equation has a variable raised to a power other than 1, such as x^2, x^3, etc., then it is not a linear equation.
3. Check for any other non-linear terms: A linear equation only contains terms involving the variable(s) being raised to a power of 1 or 0. Any term with a higher power, such as x^2, x^3, etc., or terms involving square roots, absolute values, trigonometric functions, logarithms, or any other non-linear operation, indicates a non-linear equation.
4. Ensure there are no products or divisions involving the variable: In a linear equation, the variable(s) can only be multiplied or divided by a constant value. If there are any terms involving the variable(s) being multiplied or divided together, such as x^2 * x or x / (x + 1), then it is not a linear equation.
If the equation passes all these checks, then it represents a linear relation. However, if any of these criteria are not met, then the equation describes a non-linear relation.