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Find the equation of the line parallel to 5 x = 7 + y and passing through the point ( −1 , −2 ) .

y = 5 x + 3

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Finding the equation of a line perpendicular to a given line passing through a given point

Find the equation of the line perpendicular to 5 x 3 y + 4 = 0 ( 4 , 1 ) .

The first step is to write the equation in slope-intercept form.

5 x 3 y + 4 = 0 −3 y = −5 x 4 y = 5 3 x + 4 3

We see that the slope is m = 5 3 . This means that the slope of the line perpendicular to the given line is the negative reciprocal, or 3 5 . Next, we use the point-slope formula with this new slope and the given point.

y 1 = 3 5 ( x ( −4 ) ) y 1 = 3 5 x 12 5 y = 3 5 x 12 5 + 5 5 y = 3 5 x 7 5
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Key concepts

  • We can solve linear equations in one variable in the form a x + b = 0 using standard algebraic properties. See [link] and [link] .
  • A rational expression is a quotient of two polynomials. We use the LCD to clear the fractions from an equation. See [link] and [link] .
  • All solutions to a rational equation should be verified within the original equation to avoid an undefined term, or zero in the denominator. See [link] and [link] .
  • Given two points, we can find the slope of a line using the slope formula. See [link] .
  • We can identify the slope and y -intercept of an equation in slope-intercept form. See [link] .
  • We can find the equation of a line given the slope and a point. See [link] .
  • We can also find the equation of a line given two points. Find the slope and use the point-slope formula. See [link] .
  • The standard form of a line has no fractions. See [link] .
  • Horizontal lines have a slope of zero and are defined as y = c , where c is a constant.
  • Vertical lines have an undefined slope (zero in the denominator), and are defined as x = c , where c is a constant. See [link] .
  • Parallel lines have the same slope and different y- intercepts. See [link] .
  • Perpendicular lines have slopes that are negative reciprocals of each other unless one is horizontal and the other is vertical. See [link] .

Section exercises

Verbal

What does it mean when we say that two lines are parallel?

It means they have the same slope.

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What is the relationship between the slopes of perpendicular lines (assuming neither is horizontal nor vertical)?

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How do we recognize when an equation, for example y = 4 x + 3 , will be a straight line (linear) when graphed?

The exponent of the x variable is 1. It is called a first-degree equation.

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What does it mean when we say that a linear equation is inconsistent?

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When solving the following equation:

2 x 5 = 4 x + 1

explain why we must exclude x = 5 and x = −1 as possible solutions from the solution set.

If we insert either value into the equation, they make an expression in the equation undefined (zero in the denominator).

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Algebraic

For the following exercises, solve the equation for x .

3 ( x + 2 ) 12 = 5 ( x + 1 )

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12 5 ( x + 3 ) = 2 x 5

x = 2 7

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x 3 3 4 = 2 x + 3 12

x = 6

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3 ( 2 x 1 ) + x = 5 x + 3

x = 3

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2 x 3 3 4 = x 6 + 21 4

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Questions & Answers

By the definition, is such that 0!=1.why?
Unikpel Reply
(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
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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
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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
Soo sorry (5±Root11* i)/3
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
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Jhovie
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Charmaine Reply
A banana.
Yaona
a function
Daniel
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emmanuel
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Miranda
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Propessor Reply
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Miranda
Practice Key Terms 7

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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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