The linear function y = kx + b

From two line points find the slope k = (y₂ − y₁)/(x₂ − x₁). Then b = y₁ − kx₁, giving y = kx + b. Check both axis scales when reading a graph.

Distinct parallel lines have equal slopes k and different intercepts b. Look for an equation with the same x coefficient.

Slope k gives the change in y when x increases by 1. Positive k means increase and negative k decrease. When comparing slopes, distinguish their numerical values from steepness, which depends on |k|.

Substitute the given x into y = kx + b. Multiply k by x first, then add b. For a trend line, this is a prediction rather than a guaranteed observed value.

At the intersection both lines have the same y. Solve k₁x + b₁ = k₂x + b₂, then substitute x into either equation to find y. Check the pair in both equations.

Slope k gives the change in y when x increases by 1. Positive k means increase and negative k decrease. When comparing slopes, distinguish their numerical values from steepness, which depends on |k|.

From two line points find the slope k = (y₂ − y₁)/(x₂ − x₁). Then b = y₁ − kx₁, giving y = kx + b. Check both axis scales when reading a graph.

At x = 0, all terms containing x vanish, so the y-intercept value is the constant term. In a linear cost formula it is the fixed fee; total cost = fixed fee + unit price × quantity. For a quadratic, the intercept is (0, c).

At x = 0, all terms containing x vanish, so the y-intercept value is the constant term. In a linear cost formula it is the fixed fee; total cost = fixed fee + unit price × quantity. For a quadratic, the intercept is (0, c).

From two line points find the slope k = (y₂ − y₁)/(x₂ − x₁). Then b = y₁ − kx₁, giving y = kx + b. Check both axis scales when reading a graph.