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If the graphs of two linear functions are perpendicular, describe the relationship between the slopes and the y -intercepts.

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If a horizontal line has the equation f ( x ) = a and a vertical line has the equation x = a , what is the point of intersection? Explain why what you found is the point of intersection.

The point of intersection is ( a ,   a ) . This is because for the horizontal line, all of the y coordinates are a and for the vertical line, all of the x coordinates are a . The point of intersection is on both lines and therefore will have these two characteristics.

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Algebraic

For the following exercises, determine whether the equation of the curve can be written as a linear function.

For the following exercises, determine whether each function is increasing or decreasing.

g ( x ) = 5 x + 6

Increasing

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b ( x ) = 8 3 x

Decreasing

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k ( x ) = −4 x + 1

Decreasing

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p ( x ) = 1 4 x 5

Increasing

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n ( x ) = 1 3 x 2

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m ( x ) = 3 8 x + 3

Decreasing

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For the following exercises, find the slope of the line that passes through the two given points.

( 2 , 4 ) and ( 4 , 10 )

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( 1 , 5 ) and ( 4 , 11 )

2

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( –1 , 4 ) and ( 5 , 2 )

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( 8 , –2 ) and ( 4 , 6 )

–2

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( 6 , 11 ) and ( –4 , 3 )

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For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.

f ( 5 ) = −4 , and f ( 5 ) = 2

y = 3 5 x 1

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f ( −1 ) = 4 , and f ( 5 ) = 1

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Passes through ( 2 , 4 ) and ( 4 , 10 )

y = 3 x 2

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Passes through ( 1 , 5 ) and ( 4 , 11 )

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Passes through ( −1 , 4 ) and ( 5 , 2 )

y = 1 3 x + 11 3

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Passes through ( −2 , 8 ) and ( 4 , 6 )

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x intercept at ( −2 , 0 ) and y intercept at ( 0 , −3 )

y = 1.5 x 3

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x intercept at ( −5 , 0 ) and y intercept at ( 0 , 4 )

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For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither.

4 x 7 y = 10 7 x + 4 y = 1

perpendicular

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3 y + x = 12 y = 8 x + 1

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3 y + 4 x = 12 6 y = 8 x + 1

parallel

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6 x 9 y = 10 3 x + 2 y = 1

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For the following exercises, find the x - and y- intercepts of each equation.

f ( x ) = x + 2

f ( 0 ) = ( 0 ) + 2 f ( 0 ) = 2 y int : ( 0 , 2 ) 0 = x + 2 x int : ( 2 , 0 )

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h ( x ) = 3 x 5

h ( 0 ) = 3 ( 0 ) 5 h ( 0 ) = 5 y int : ( 0 , 5 ) 0 = 3 x 5 x int : ( 5 3 , 0 )

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2 x + 5 y = 20

2 x + 5 y = 20 2 ( 0 ) + 5 y = 20 5 y = 20 y = 4 y int : ( 0 , 4 ) 2 x + 5 ( 0 ) = 20 x = 10 x int : ( 10 , 0 )

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For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?

Line 1: Passes through ( 0 , 6 ) and ( 3 , −24 )

Line 2: Passes through ( −1 , 19 ) and ( 8 , −71 )

Line 1: m = –10 Line 2: m = –10 Parallel

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Line 1: Passes through ( −8 , −55 ) and ( 10 , 89 )

Line 2: Passes through ( 9 , 44 ) and ( 4 , 14 )

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Line 1: Passes through ( 2 , 3 ) and ( 4 , −1 )

Line 2: Passes through ( 6 , 3 ) and ( 8 , 5 )

Line 1: m = –2 Line 2: m = 1 Neither

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Line 1: Passes through ( 1 , 7 ) and ( 5 , 5 )

Line 2: Passes through ( −1 , −3 ) and ( 1 , 1 )

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Line 1: Passes through ( 2 , 5 ) and ( 5 , 1 )

Line 2: Passes through ( −3 , 7 ) and ( 3 , −5 )

Line 1 :   m = 2       Line 2 :   m = 2       Parallel

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For the following exercises, write an equation for the line described.

Write an equation for a line parallel to f ( x ) = 5 x 3 and passing through the point ( 2 , 12 ) .

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Write an equation for a line parallel to g ( x ) = 3 x 1 and passing through the point ( 4 , 9 ) .

y = 3 x 3

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Questions & Answers

(1+cosA+IsinA)(1+cosB+isinB)/(cos@+isin@)(cos$+isin$)
Ajay Reply
hatdog
Mark
how we can draw three triangles of distinctly different shapes. All the angles will be cutt off each triangle and placed side by side with vertices touching
Shahid Reply
bsc F. y algebra and trigonometry pepper 2
Aditi Reply
given that x= 3/5 find sin 3x
Adamu Reply
4
DB
remove any signs and collect terms of -2(8a-3b-c)
Joeval Reply
-16a+6b+2c
Will
is that a real answer
Joeval
(x2-2x+8)-4(x2-3x+5)
Ayush Reply
sorry
Miranda
x²-2x+9-4x²+12x-20 -3x²+10x+11
Miranda
x²-2x+9-4x²+12x-20 -3x²+10x+11
Miranda
(X2-2X+8)-4(X2-3X+5)=0 ?
master
The anwser is imaginary number if you want to know The anwser of the expression you must arrange The expression and use quadratic formula To find the answer
master
The anwser is imaginary number if you want to know The anwser of the expression you must arrange The expression and use quadratic formula To find the answer
master
Y
master
X2-2X+8-4X2+12X-20=0 (X2-4X2)+(-2X+12X)+(-20+8)= 0 -3X2+10X-12=0 3X2-10X+12=0 Use quadratic formula To find the answer answer (5±Root11i)/3
master
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master
x2-2x+8-4x2+12x-20 x2-4x2-2x+12x+8-20 -3x2+10x-12 now you can find the answer using quadratic
Mukhtar
2x²-6x+1=0
Ife
explain and give four example of hyperbolic function
Lukman Reply
What is the correct rational algebraic expression of the given "a fraction whose denominator is 10 more than the numerator y?
Racelle Reply
y/y+10
Mr
Find nth derivative of eax sin (bx + c).
Anurag Reply
Find area common to the parabola y2 = 4ax and x2 = 4ay.
Anurag
y2=4ax= y=4ax/2. y=2ax
akash
A rectangular garden is 25ft wide. if its area is 1125ft, what is the length of the garden
Jhovie Reply
to find the length I divide the area by the wide wich means 1125ft/25ft=45
Miranda
thanks
Jhovie
What do you call a relation where each element in the domain is related to only one value in the range by some rules?
Charmaine Reply
A banana.
Yaona
given 4cot thither +3=0and 0°<thither <180° use a sketch to determine the value of the following a)cos thither
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Mark Reply
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Miranda
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Miranda
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Propessor Reply
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
Miranda
state and prove Cayley hamilton therom
sita Reply
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Propessor
hi
Miranda
the Cayley hamilton Theorem state if A is a square matrix and if f(x) is its characterics polynomial then f(x)=0 in another ways evey square matrix is a root of its chatacteristics polynomial.
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jai
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Propessor
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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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