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TEACHER:
Mr. Landry  ROOM NUMBER: 111
landrg@portlandschools.org

 

GENERAL TOPIC
X AND Y INTERCEPTS

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WHAT I WILL ASSUME
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I am going to assume that you can plot a set of ordered pairs as points on a Cartesian Coordinate System. If you are unsure how to plot ordered pairs please go the the column on your right and see the EXTRAS area.

COMMENT: You have also seen y-intercepts(vertical intercepts). But I need to review this for the upcoming sections.

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VERTICAL INTERCEPTS AND HORIZONTAL
INTERCEPTS

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In figure 1 below you can see a line with two points on it. The line intersects the x axis at the point (-4,0) and intersects the y axis at the point (0,2).

The x value, -4, of the point on the line that intersects the x axis is called the x-intercept or the horizontal intercept. Some math books will say the x intercept is (-4, 0).

The y value, 2, of the point on the line that intersects the y axis is called the y-intercept or the vertical intercept. Some math books will say the y intercept is (0, 2).

We are reviewing these concepts as it will be very important that you understand how to name the x and y intercepts, also called the horizontal and vertical intercepts, in some upcoming exercises.


figure 1
Figure

If the axes are named by other variables than x and y then you would not use the words x intercept or y intercept as we did above. See figure 2 below. In this case I would say the h intercept is 3 and the s intercept is -2.

figure 2
Figure


example 1) Name the x and y intercept from the figure below.


Figure

ans: The x intercept is -5 and the y intercept is 3.

example 2) Name the z intercept(vertical intercept) and w intercept(horizontal intercept) from the figure below.


Figure

ans: The w intercept is -1 and the z intercept is -3.


example 3) Name the vertical and horizontal intercept from the figure below.


Figure

ans: The vertical intercept(k-intercept) is -4.5 and the horizontal intercept(q intercept) is 5.1.

 

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HOW TO FIND VERTICAL AND HORIZONTAL
INTERCEPTS WITHOUT GRAPHING

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If you have an equation of a line in slope intercept form then you can find the x intercept and y intercept very easily. I will do 3 examples.

 

example 1) Given the equation of the line $\ y=3x+6$ in slope intercept form determine the x and y intercept, then graph $y=3x+6$ using the x and y intercept.

ans: You know the y intercept(vertical intercept) is 6 based on the slope intercept form of a line.


Figure

Please note that 6 is also called the vertical intercept.

To get the x-intercept all you have to do is set y equal to 0 and solve for x.

$0=3x+6$ OR $3x+6=0$

$3x+6=0$

$3x+6-6=0-6$

$3x=-6$

MATH

$x=-2$ This is the x intercept

Please note that -2 is also called the horizontal intercept.

Here is the graph:

Figure

example 2) Given the equation of the line $\ y=-2x-8$ in slope intercept form determine the x and y intercept, then graph $y=-2x-8$ using the x and y intercept.

ans: You know the y intercept(vertical intercept) is -8 based on the slope intercept form of a line.


Figure

To get the x-intercept all you have to do is set y equal to 0 and solve for x.

$0=-2x-8$ OR $-2x-8=0$

$-2x-8=0$

$-2x-8+8=0+8$

$-2x=8$

MATH

$x=-4$

$x=-4$  This is the x intercept

 

Here is the graph:


Figure

example 3) Given the equation of the line $\ s=5t+10$ in slope intercept form determine the t and s intercept, then graph $s=5t+10$ using the t and s intercept.

answer: The s intercept is 10. This is also called the vertical intercept.


Figure

To find the t intercept set s=0 and solve for t.

$0=5t+10$ or $5t+10=0$

$5t+10=0$

$5t+10-10=0-10$

$5t=-10$

MATH

$t=-2$  is the t intercept

Here is the graph:


Figure

HOMEWORK

DIRECTIONS - GIVEN THE FOLLOWING EQUATIONS IN SLOPE INTERCEPT FORM DETERMINE THE VERTICAL AND HORIZONTAL INTERCEPT THEN GRAPH THE EQUATION USING THE INTERCEPTS.

1) $y=3x+12$ 2) $y=-2x-14$ 3) $y=4x-20$
4) $y=-7x+14$ 5) $y=-5x-15$ 6) $y=6x+18$
7) $s=3t-24$ 8) $s=-8t+16$ 9) $s=9t-18$

 

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BACK TO ALGEBRA 1 PART 2 CURRICULUM


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EXTRAS
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... MULTIPLICATION AND PARENTHESES

- PRIME FACTORIZATION

... ORDER OF OPERATIONS
PART 1: PART 2 : PART 3

... MONOMIAL,TERMS AND FACTORS

... THE WORLD OF EXPONENTS

... ADDING SIGNED NUMBERS ON A NUMBER LINE

...VARIABLES: 4 PARTS
PART 1 | PART 2 | PART 3 | PART 4

... ABSOLUTE VALUE

... USING DUDE TO ADD INTEGERS

... USING DUDE TO SUBTRACT INTEGERS

... CARTESIAN COORDINATE SYSTEM:
PART 1 : PART 2 : PART 3  : PART 4 : PART 5
more to come

GEOGEBRA EXERCISES: ADDING LIKE TERMS

  1. ADDING LIKE TERMS 1

  2. ADDING LIKE TERMS 2

GEOGEBRA EXERCISES: EVALUATE AN ALGEBRAIC EXPRESSION

  1. EVALUATE  ALGEBRAIC EXPRESSION 1

  2. EVALUATE ALGEBRAIC EXPRESSION 2

  3. EVALUATE ALGEBRAIC EXPRESSION 3

...GEOGEBRA EXERCISE: SLOPE OF A LINE

...GEOGEGRA EXERCISE: BEST FIT LINE

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TI 83/84
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- BASIC GRAPHING - PART 1 : more to come