# 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.

1. Write an equation that describes the relationship between $$h$$ and $$t$$.
2. 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 $$y=\frac74x$$

1. If you used 4 cups of sugar, how much flour does each recipe need?
2. What is the constant of proportionality for each situation and what does it mean?
(From Unit 5, Lesson 3.)

### 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.