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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

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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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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