Lesson 10

Solutions to Linear Equations

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Problem 1

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

A:

\((0,2)\)

B:

\((0,6)\)

C:

\((2,3)\)

D:

\((3,\text-2)\)

E:

\((3,0)\)

F:

\((6,\text-2)\)

Solution

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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.

Graph of a line, origin O, with grid.
  1. Find and interpret the \(x\)- and \(y\)-intercepts of this line.
     
  2. Find and interpret the slope of this line.
     
  3. Find an equation for this line.
  4. If Priya buys 3 comics, how much money will she have remaining?

Solution

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Problem 3

Match each equation with its three solutions.

A:

\(y = 1.5x\)

B:

\(2x + 3y = 7\)

C:

\(x - y = 4\)

D:

\(3x = \frac y2\)

E:

\(y = \text-x + 1\)

1:

\((14, 21)\), \((2,3)\), \((8,12)\)

2:

\((\text-3, \text-7)\), \((0, \text-4)\), \((\text-1,\text-5)\)

3:

\(\left(\frac 18, \frac78\right), \left(\frac 12,\frac 12\right), \left(\frac 14, \frac 34\right)\)

4:

\(\left(1, 1\frac23\right), \left(\text-1,3\right), \left(0, 2\frac13\right)\)

5:

\((0.5,3)\), \((1,6)\), \((1.2, 7.2)\)

Solution

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Problem 4

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.

Solution

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(From Unit 5, Lesson 9.)

Problem 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.

Solution

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(From Unit 5, Lesson 4.)