Understanding Mathematical Terms

Refer to the English-Spanish Glossary, which starts on textbook page A39, if you need help with a definition or finding a textbook page with an example for a vocabulary word.

Explorations

Read and work through the Explorations 1 and 2 and Communicate Your Answer on page 173. One technique you will use is to first use the given information to write a linear equation in slope-intercept form and point-slope form. Then, using symbolic manipulation, the equation is rewritten in standard form. Then, check your answers below.

Answers to Explorations and Communicate Your Answer

Exploration 1 (page 173)

1. y – 3x = –5; –3x + y = –5
2. y – 4 = –2x – 12;
   y – 4 + 2x = –12;
   y + 2x = –8; 2x + y = –8
3. –4x + y = 2
4. x + y = –7
5. –3x + y = 13
6. 4x + y = 4

Exploration 2 (page 173)

1. 3y = 6x – 15; y = 2x – 5; 2; –5
2. slope: ; y-intercept: 4
3. slope: ; y-intercept: –7

Communicate Your Answer (page 173)

3. Write the equation in the form Ax + By – C.
4. Rewrite the equation in slope-intercept form.
5. a. yes; yes; Changing the value of A changes the numerator of the slope and changing the value of B changes the denominator of the slope.
   b. no; yes; The y-intercept is only affected by the values of B and C because the y-intercept is given by .

Section 4-3 Lesson (pages 174-176)

Read and study Examples 1 through 5. Look carefully at the information you are given in each example. Standard Form seems to be hard at times. You need to remember all your rules for solving equations. Keep your equations balanced. Take your time. Practice with the Monitoring Progress problems as you go, and then check your answers below.

Answers to Monitoring Progress (pages 174-176)

1. Sample answer: 2x – 2y = 6,    –    = 1
2. –2x + y = –7
3. y = –9, x = –8
4. y = –5, x = 13
5. 3; –4x + 3y = 7
6. –7; –7x + y = –3
7. 8s + 12l = 136; Sample answer: 2 small vans and 10 large vans, 5 small vans and 8 large vans, 8 small vans and 6 large vans, and 11 small vans and 4 large vans