Functions are a lot like equations. In a function we look at the relationship of the variables. Does one variable depend on the other.
In a function when you see f(x) it just means "y." So we have an equation y = 2x + 3 and a function that is
f(x) = 2x + 3. When graphed, they both look like the same line.
What makes these a linear equation or a linear function? How can we tell if they are linear?
The "x" is the one make a linear function or equation. Cuz x is independent variable and we just plug it in equation to find y or f(x).
Linear equation has formula: y=ax+b
Unlike parabola: y=ax^2+bx+c and so on.
z=4x+3y
2x+3y<=6
3x-2y<=9
x+5y<=20
x>=0,y>=0
A linear equation or function is one that represents a straight line when graphed. To determine if an equation or function is linear, you can follow these steps:
1. Check the highest power of the variable: In a linear equation or function, the highest power of the variable should be 1. In other words, the variable(s) should not be raised to any power higher than 1 (e.g., x^2, x^3, etc.).
2. Look for any other operations involving the variable: In a linear equation or function, the variable(s) should only appear with coefficients (numbers multiplying the variable) and with addition or subtraction operations. Multiplication, division, and addition or subtraction of constant terms are allowed as well.
In the given example, the equation y = 2x + 3 can also be written as f(x) = 2x + 3. Both are linear equations/functions because:
1. The highest power of the variable (x) is 1.
2. The variable (x) appears with a coefficient (2) and an addition operation (+ 3).
When graphed, both equations/functions will represent a straight line.