Linear Functions and Their Forms

Linear functions follow the pattern f(x) = a + bx and always create straight lines on a graph. The way we write these functions can change depending on what information we have and what we need to solve.

The standard form of a linear equation looks like Ax + By = C, where A, B, and C are integers. This form is useful when working with systems of equations or when you need to find intercepts.

The slope-intercept form is y = mx + b, where m represents the slope (how steep the line is) and b is the y-intercept $where the line crosses the y-axis$. This is probably the most common form you'll use because it makes graphing quick and easy!

💡 Think of slope (m) as "rise over run" - it tells you how much the line rises (or falls) vertically when you move horizontally. A positive slope means the line goes up from left to right, while a negative slope means it goes down.

The point-slope form is written as y - y₁ = m$x - x₁$, where m is the slope and (x₁, y₁) is a point on the line. This form is super helpful when you know one point on the line and the slope, but don't know the y-intercept yet.