Lesson 12: Practice Problems

Problem 1

Select all of the ordered pairs $(x, y)$ that are solutions to the linear equation $2 x + 3 y = 6$ .

$(0, 2)$
$(0, 6)$
$(2, 3)$
$(3, - 2)$
$(3, 0)$
$(6, - 2)$

Problem 2

The graph shows a linear relationship between $x$ and $y$ .

$x$ represents the number of comic books Priya buys at the store, all at the same price, and $y$ represents the amount of money (in dollars) Priya has after buying the comic books.

A graph of x (comics) vs y (dollars) with a line starting at (0,20) and ending at (5,0)

Find and interpret the $x$ - and $y$ -intercepts of this line.
Find and interpret the slope of this line.
Find an equation for this line.
If Priya buys 3 comics, how much money will she have remaining?

Problem 3

Match each equation with its three solutions.

$y = 1.5 x$
$2 x + 3 y = 7$
$x - y = 4$
$3 x = \frac{y}{2}$
$y = - x + 1$

$(14, 21)$ , $(2, 3)$ , $(8, 12)$
$(- 3, - 7)$ , $(0, - 4)$ , $(- 1, - 5)$
$(\frac{1}{8}, \frac{7}{8}), (\frac{1}{2}, \frac{1}{2}), (\frac{1}{4}, \frac{3}{4})$
$(1, 1 \frac{2}{3})$ , $(- 1, 3)$ , $(0, 2 \frac{1}{3})$
$(0.5, 3)$ , $(1, 6)$ , $(1.2, 7.2)$

Problem 4 From Unit 3 Lesson 10

A container of fuel dispenses fuel at the rate of 5 gallons per second. If $y$ represents the amount of fuel remaining in the container, and $x$ represents the number of seconds that have passed since the fuel started dispensing, then $x$ and $y$ satisfy a linear relationship.

In the coordinate plane, will the slope of the line representing that relationship have a positive, negative, or zero slope? Explain how you know.

Problem 5 From Unit 3 Lesson 5

A sandwich store charges a delivery fee to bring lunch to an office building. One office pays $33 for 4 turkey sandwiches. Another office pays $61 for 8 turkey sandwiches. How much does each turkey sandwich add to the cost of the delivery? Explain how you know.