GRAPH PROPORTIONAL RELATIONSHIPS Section 1 5 Vocabulary Maps

GRAPH PROPORTIONAL RELATIONSHIPS Section 1. 5

Vocabulary • Maps have grids to locate cities. The _______ is a type of grid that is formed when two number lines intersect at their zero points. • The number lines separate the coordinate plane into four regions called ______. • An _____ is a pair of numbers, such as (1, 2), used to locate or graph points on the coordinate plane.

Vocabulary • The _____ corresponds to a number on the x-axis. • The _____ corresponds to a number on the y-axis.

Coordinate Plane • Label the coordinate plane with the terms: ordered pair, x- coordinate, and y-coordinate. Quadrant 2 Quadrant 1 (1, 2) Quadrant 3 Quadrant 4

Identify Proportional Relationships • Another way to determine whether two quantities are proportional is to graph the quantities on the coordinate plane. • If the graph of the two quantities is a straight line through the origin, then the two quantities are proportional.

Example • 1. The slowest mammal on Earth is the tree sloth. It moves at a speed of 6 feet per minute. Determine whether the number of feet the sloth moves is proportional to the number of minutes it moves by graphing on the coordinate plane. Explain your reasoning.

Example • Step 1: Make a table to find the number of feet walked for 0, 1, 2, 3, and 4 minutes. Time (minutes) 0 1 Distance (feet) 0 6 2 3 4

Example • Step 2: Graph the ordered pairs (time, distance) on the coordinate plane. Then connect the ordered pairs.

Example • Does the line pass though the origin? • Does it form a straight line? • If the answers are both yes, then the relationship is proportional.

On your Own • 2. James earns $5 an hour babysitting. Determine whether the amount of money James earns babysitting is proportional to the number of hours he babysits by graphing on the coordinate plan. Explain your reasoning.

Essential Question • How does graphing relationships help you determine whether the relationship is proportional or not? • ______________________________________________