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ACCELERATED PRE-CALCULUS SUMMER STUDY GUIDE

CHAPTER 14: X-INTERCEPT(ZERO) AND Y INTERCEPT(B)


 

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SECTION 14.1: THE X AND Y INTERCEPT, THE ZERO
AND THE SYMBOL b
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When a line crosses either the x-axis and or y-axis, it crosses the axes at a particular point. In figure 1 below, the line crosses the x-axis at the point at (-3, 0) and the y-axis at (0, 3).

figure 1
figure 1


The x-value of the point on the line that crosses the x-axis is called the "x intercept" or the "zero." The "x-intercept" or "zero" in figure 1 is x = -2.

The y-value of the point on the line that crosses the y-axis is called the "y-intercept." The "y-intercept" in the above graph is y = 3. Mathematicians have decided to name the y-intercept with the lower case letter "b." So in figure 1, the y-intercept would be labeled b = 3.

There is no special letter to name the x-intercept, though as stated above, the x-intercept has a special name called the "zero" or the "root."

HERE ARE SOME MORE EXAMPLES:

FIGURE 2

y-intercept also labeled b = 4

 

FIGURE 3

y-intercept also labeled b = -5

 

FIGURE 4  

FIGURE 5

y-intercept also labeled b = 7

 

FIGURE 6  

FIGURE 7

y-intercept also labeled b = -5

 

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THE SUMMER STUDY GUIDE
BY CHAPTERS

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RETURN TO THE SUMMER STUDY GUIDE MAIN PAGE

- CHAPTER 1: THE NUMBER SYSTEM

- CHAPTER 2: ORDER OF OPERATIONS

- CHAPTER 3: VARIABLES, MONOMIALS, BINOMIALS, TRINOMIALS, POLYNOMIALS,
COEFFICIENTS, TERMS AND LIKE TERMS

- CHAPTER 4: SIGNED NUMBERS, ABSOLUTE VALUE, AND INEQUALITY SYMBOLS

- CHAPTER 5: FACTORS, COMMON FACTORS, LEAST COMMON FACTORS AND GREATEST COMMON FACTORS

- CHAPTER 6: PROPERTIES OF NUMBERS

- CHAPTER 7: THE WORLD OF FRACTIONS

- CHAPTER 8: EXPONENTS

- CHAPTER 9: ROOTS

- CHAPTER 10: ALGEBRAIC EXPRESSIONS

- CHAPTER 11: CARTESIAN COORDINATE SYSTEM

- CHAPTER 12: SETS, RELATIONS AND FUNCTIONS

- CHAPTER 13: AVERAGE RATE OF CHANGE OF Y WITH RESPECT TO X, SLOPE, PYTHAGOREAN THEOREM, AND DISTANCE FORMULA BETWEEN TWO POINTS

- CHAPTER 14: X-INTERCEPT(ZERO) AND Y INTERCEPT(B)

- CHAPTER 15: LINES

- CHAPTER 16: FUNCTIONS

- CHAPTER 17: MULTIPLYING POLYNOMIALS

- CHAPTER 18: FACTORING

- CHAPTER 19: RATIONAL EXPRESSIONS

- CHAPTER 20: SOLVING EQUATIONS

- CHAPTER 21:SOLVING INEQUALITIES

- CHAPTER 22: SOLVING A SYSTEM OF EQUATIONS

- CHAPTER 23: QUADRATICS

- CHAPTER 24: CIRCLES

- CHAPTER 25: AREAS AND PERIMETERS OF PLANE FIGURES

- CHAPTER 26: VOLUMES