# Lesson 6

Representations of Linear Relationships

Let’s write equations from real situations.

### Problem 1

Create a graph that shows three linear relationships with different \(y\)-intercepts using the following slopes, and write an equation for each line.

Slopes:

- \(\frac15\)
- \(\frac35\)
- \(\frac65\)

### Problem 2

The graph shows the height in inches, \(h\), of a bamboo plant \(t\) months after it has been planted.

- Write an equation that describes the relationship between \(h\) and \(t\).
- After how many months will the bamboo plant be 66 inches tall? Explain or show your reasoning.

### Problem 3

Here are recipes for two different banana cakes. Information for the first recipe is shown in the table.

sugar (cups) | flour (cups) |
---|---|

\(\frac12\) | \(\frac34\) |

\(2\frac12\) | \(3\frac34\) |

3 | \(4\frac12\) |

The relationship between cups of flour \(y\) and cups of sugar \(x\) in the second recipe is \(y=\frac74x\)

- If you used 4 cups of sugar, how much flour does each recipe need?
- What is the constant of proportionality for each situation and what does it mean?

### Problem 4

Show that the two figures are similar by identifying a sequence of translations, rotations, reflections, and dilations that takes the larger figure to the smaller one.