- Tables, Graphs, Functions and Sequences
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- Making a table and plotting points given a unit rate
- Graphing whole number functions
- Function tables with two-step rules
- Writing a function rule given a table of ordered pairs: One-step rules
- Graphing a line in quadrant 1
- Interpreting a line graph
- Finding outputs of a one-step function that models a real-world situation
- Finding outputs of a two-step function with decimals that models a real-world situation
- Writing and evaluating a function that models a real-world situation: Basic
- Graphing ordered pairs and writing an equation from a table of values in context
- Writing an equation and drawing its graph to model a real-world situation: Basic
- Identifying independent and dependent quantities from tables and graphs
- Finding the next terms of an arithmetic sequence with whole numbers
- Finding the next terms of a geometric sequence with whole numbers
- Finding patterns in shapes

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# Graphing a line in quadrant 1

We graph a line whose equation is given, say for example y = 3x. We need at least two points or ordered pairs to graph the line. First we choose some x values. Then we evaluate y = 3x for each value of x.

For example for x = 0, y = 3(0) = 0; x = 1, y = 3(1) = 3 and so on. We put the x, y and the ordered pair (x, y) values as follows.

x | y | (x,y) |
---|---|---|

0 | 3(0) = 0 | (0,0) |

1 | 3(1) = 3 | (1,3) |

2 | 3(2) = 6 | (2,6) |

3 | 3(3) = 9 | (3,9) |

4 | 3(4) = 12 | (4,12) |

We see that the ordered pairs lie in the quadrant 1. Joining the points will give the graph of the line in quadrant 1.

Graph the line in the quadrant 1, whose equation is given below.

2x – y = 3

### Solution

**Step 1:**

Given equation 2x – y = 3; for y = 0, x = 3/2; for x = 2, y = 2(2)–3 = 4–3 = 1. So two ordered pairs are (3/2, 0) (2, 1)

**Step 2:**

Plotting the points and joining with a line we get

Graph the line in the quadrant 1, whose equation is given below.

x + 3y = 1

### Solution

**Step 1:**

Given equation x + 3y = 1; for y = 0, x = 1; For x = 0, y = 1/3. So two ordered pairs are (1, 0) and (0, 1/3)

**Step 2:**

Plotting the points and joining with a line we get