Lesson 6: Practice Problems

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:

$\frac{1}{5}$

$\frac{3}{5}$

$\frac{6}{5}$

Problem 2

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

A line graphed on the x y plane with the origin labeled O. The horizontal axis is labeled t, in months, with the numbers 1 through 15 indicated. The vertical axis is labeled h, in inches, with the numbers 5 through 50, in increments of 5, indicated. The line begins on the vertical axis at 12, slants upward and to the right passing through the points 1 comma 15, 6 omma 30, and 11 comma 45.

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 From Unit 5 Lesson 3

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

sugar (cups)	flour (cups)
$\frac{1}{2}$	$\frac{3}{4}$
$2 \frac{1}{2}$	$3 \frac{3}{4}$
$3$	$4 \frac{1}{2}$

The relationship between cups of flour $y$ and cups of sugar $x$ in the second recipe is $y = \frac{7}{4} x$

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 From Unit 2 Lesson 11

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.

Two figures, ABCD and a larger version EFGH