2.1 Review When variables change together, their interaction is called a ___________. When one variable determines the exact value of a second variable, their relation is called a ____________. The parts of a function are called _________ and output. The input is the ____________, non-repeating quantity. The output is the dependent ___________. For each input, there is a ________ output. Function Notation: Is the relation between cars and tires a function? What about houses and tenants?

Function or not? Why? Remember, when a single input can produce multiple outputs, the relation is not a function. X values cannot be repeated in a function.

Which of the following is a set of ordered pairs representing a function? B) {(0, 0), (1, 1), (1, -1), (2, 2), (2, -2)} C) (4, 2), (5, 1), (6, 0), (7, -1), (8, -2) D) {(-2, 2), (-1, 1), (0, 0), (1, 1), (2, 2)} ANSWER D

All horizontal lines represent a function. Why All horizontal lines represent a function. Why? What about vertical lines? ANSWER A line on the coordinate plane is horizontal when every x-coordinate has the same y-coordinate. No x-coordinates have more than one y-coordinate, and each input always produces the same output. Vertical lines do not represent a function because one x value is paired with many y values.

2.1 Review Graph the equation y = 3x - 2 x -2 -1 1 2 y -8 -5 4

2.1 Review Graph the equation y = -1/2x +1 x -2 -1 1 2 y 1.5 0.5

2.1 Review g(-2) = -4 – 2(-2) = -4 – -4 = -4 + 4 = 0 Tell whether the function is linear, then evaluate it when x = -2 g(x) = -4 – 2x Yes, the function is linear. Why? g(-2) = -4 – 2(-2) = -4 – -4 = -4 + 4 = 0

EXAMPLE 2 Standardized Test Practice SOLUTION Let (x1, y1) = (–1, 3) and (x2, y2) = (2, –1). m = y2 – y1 x2 – x1 = – 1 – 3 2 – (–1) = 4 3 ANSWER The correct answer is A.

GUIDED PRACTICE for Examples 1 and 2 6. (7, 3), (– 1, 7) SOLUTION Let (x1, y1) = (7, 3) and (x2, y2) = (– 1, 7). m = y2 – y1 x2 – x1 = 7 – 3 – 1 – 7 = 1 2 – ANSWER 1 2 –

Classify lines using slope EXAMPLE 3 Classify lines using slope Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical. a. (– 5, 1), (3, 1) b. (– 6, 0), (2, –4) c. (–1, 3), (5, 8) d. (4, 6), (4, –1) SOLUTION 1 – 1 3– (–5) = m = a. 8 = 0 Because m = 0, the line is horizontal. – 4 – 0 2– (–6) = m = b. – 4 8 = 1 2 – Because m < 0, the line falls.

Classify lines using slope EXAMPLE 3 Classify lines using slope Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical. a. (– 5, 1), (3, 1) b. (– 6, 0), (2, –4) c. (–1, 3), (5, 8) d. (4, 6), (4, –1) SOLUTION 1 – 1 3– (–5) = m = a. 8 = 0 Because m = 0, the line is horizontal. – 4 – 0 2– (–6) = m = b. – 4 8 = 1 2 – Because m < 0, the line falls.

a. b. EXAMPLE 4 Classify parallel and perpendicular lines Tell whether the lines are parallel, perpendicular, or neither. Line 1: through (– 2, 2) and (0, – 1) a. Line 2: through (– 4, – 1) and (2, 3) Line 1: through (1, 2) and (4, – 3) b. Line 2: through (– 4, 3) and (– 1, – 2) SOLUTION Find the slopes of the two lines. a. m1 = –1 – 2 0 – (– 2) = – 3 2 3 2 –

EXAMPLE 4 Classify parallel and perpendicular lines m2 = 3 – (– 1) 2 – (– 4) = 4 6 2 3 ANSWER Because m1m2 = – 2 3 = – 1, m1 and m2 are negative reciprocals of each other. So, the lines are perpendicular.

EXAMPLE 4 Classify parallel and perpendicular lines Find the slopes of the two lines. b. m1 = –3 – 2 4 – 1 = – 5 3 = 5 3 – m2 = – 2 – 3 – 1 – (– 4) = – 5 3 = 5 3 – ANSWER Because m1 = m2 (and the lines are different), you can conclude that the lines are parallel.