3B Ratio Tables & Graphs Study Guide

📘 Key Vocabulary

Ratio Table — a table that shows pairs of numbers that have the same ratio. (tabla de razones)

Equivalent Ratio — two ratios that are equal; they make the same comparison. (razón equivalente)

Coordinate Graph — a grid with an x-axis (horizontal) and a y-axis (vertical) used to plot points. (gráfico de coordenadas)

Ordered Pair — a pair of numbers (x, y) that shows a point on a coordinate graph. (par ordenado)

Origin — the point (0, 0) where the x-axis and y-axis cross. (origen)

📋 Visual Example — Ratio Table

A recipe uses 2 cups of flour for every 3 cups of milk. Build a ratio table:

Flour (cups)	2	4	6	8	10
Milk (cups)	3	6	9	12	15

Pattern: Each column is found by multiplying both parts of the ratio by the same number.
×1 → (2, 3) | ×2 → (4, 6) | ×3 → (6, 9) | ×4 → (8, 12) | ×5 → (10, 15)

📈 Plotting Ratios on a Coordinate Graph

Each column in the ratio table becomes an ordered pair (x, y) on the graph:

(2, 3) (4, 6) (6, 9) (8, 12) (10, 15)

  y (Milk)
  15 |                         *
  12 |                   *
   9 |             *
   6 |       *
   3 | *
   0 +---+---+---+---+---+--- x (Flour)
     0   2   4   6   8  10

Key idea: If the points form a straight line through the origin (0,0), the ratios are equivalent!

🔢 Step-by-Step — Extending a Ratio Table

1 Identify the starting ratio from the first column.
2 Multiply both parts of the ratio by the same number to find the next column.
3 Repeat to fill in more columns.
4 To go backwards (make smaller), divide both parts by the same number.

Example: Ratio is 5 : 2. Fill in the table.

x	5	10	15	20
y	2	4	6	8

Each column: multiply both by 1, 2, 3, 4...

📐 Formula Box

To extend a ratio table: Multiply (or divide) BOTH parts by the SAME number

Ordered Pair = (first quantity, second quantity) = (x, y)

Equivalent ratios form a straight line through the origin on a graph

⚠️ Watch Out!

You must multiply or divide BOTH parts of the ratio by the same number. Changing only one side breaks the ratio!
On a graph, x comes first, y comes second in an ordered pair (x, y). Don't mix them up!
The line must go through (0, 0) for equivalent ratios. If it doesn't pass through the origin, the relationship is not a proportional ratio.
Adding the same number to both parts does NOT keep the ratio equivalent. You must multiply or divide.

✏️ Practice Problems

1. Complete the ratio table. The ratio is 3 : 4.

x	3	6	9	?
y	4	8	12	?

What are the missing values? Type as: x,y (example: 12,16)

2. The ratio of pencils to erasers is 5 : 2. If there are 20 pencils, how many erasers are there?

3. Complete the ratio table. The ratio is 7 : 3.

x	7	14	?
y	3	6	?

What are the missing values? Type as: x,y

4. Which ordered pair belongs on the graph of the ratio 2 : 5?

A) (4, 10) B) (4, 7) C) (6, 14) D) (3, 8)