Key Terms
Linear function
A function with a constant rate of change; polynomial of degree 1; graph is a straight line.
Equation form
Y = mx + b
Function notation
F(x) = mx + b
Units
Always output units per input unit. Examples: dollars per day; meters per second; people per year.
Subtract x-values (input) in the same order
X2 - x1 4. Divide.
Points
(5, 1) and (8, 7) Step 1: m = (7 - 1) / (8 - 5) = 6 / 3 = 2 Step 2: y - 1 = 2(x - 5) y - 1 = 2x - 10 y = 2x - 9
To write the equation
Plug m and b straight into f(x) = mx + b. Done.
To convert point-slope to slope-intercept
Distribute and solve for y.
Fixed costs
Costs that do not change with the number of units produced.
Break-even
The point where revenue equals cost. No profit, no loss.
Slope
Ratio of change in output to change in input; measures steepness and direction of a line.
Slope-intercept form
F(x) = mx + b; m is slope, b is y-intercept.
Point-slope form
Y - y1 = m(x - x1); uses slope and one known point.
Increasing linear function
M > 0; output rises as input rises.
Decreasing linear function
M < 0; output falls as input rises.