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A line passes through the points, ( −2 , −15 ) and ( 2 , −3 ) . Find the equation of a perpendicular line that passes through the point, ( 6 , 4 ) .

y = 1 3 x + 6

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Access this online resource for additional instruction and practice with linear functions.

Key concepts

  • Linear functions can be represented in words, function notation, tabular form, and graphical form. See [link] .
  • An increasing linear function results in a graph that slants upward from left to right and has a positive slope. A decreasing linear function results in a graph that slants downward from left to right and has a negative slope. A constant linear function results in a graph that is a horizontal line. See [link] .
  • Slope is a rate of change. The slope of a linear function can be calculated by dividing the difference between y -values by the difference in corresponding x -values of any two points on the line. See [link] and [link] .
  • An equation for a linear function can be written from a graph. See [link] .
  • The equation for a linear function can be written if the slope m and initial value b are known. See [link] and [link] .
  • A linear function can be used to solve real-world problems given information in different forms. See [link] , [link] , and [link] .
  • Linear functions can be graphed by plotting points or by using the y -intercept and slope. See [link] and [link] .
  • Graphs of linear functions may be transformed by using shifts up, down, left, or right, as well as through stretches, compressions, and reflections. See [link] .
  • The equation for a linear function can be written by interpreting the graph. See [link] .
  • The x -intercept is the point at which the graph of a linear function crosses the x -axis. See [link] .
  • Horizontal lines are written in the form, f ( x ) = b . See [link] .
  • Vertical lines are written in the form, x = b . See [link] .
  • Parallel lines have the same slope. Perpendicular lines have negative reciprocal slopes, assuming neither is vertical. See [link] .
  • A line parallel to another line, passing through a given point, may be found by substituting the slope value of the line and the x - and y -values of the given point into the equation, f ( x ) = m x + b , and using the b that results. Similarly, the point-slope form of an equation can also be used. See [link] .
  • A line perpendicular to another line, passing through a given point, may be found in the same manner, with the exception of using the negative reciprocal slope. See [link] and [link] .

Section exercises

Verbal

Terry is skiing down a steep hill. Terry's elevation, E ( t ) , in feet after t seconds is given by E ( t ) = 3000 70 t . Write a complete sentence describing Terry’s starting elevation and how it is changing over time.

Terry starts at an elevation of 3000 feet and descends 70 feet per second.

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Jessica is walking home from a friend’s house. After 2 minutes she is 1.4 miles from home. Twelve minutes after leaving, she is 0.9 miles from home. What is her rate in miles per hour?

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A boat is 100 miles away from the marina, sailing directly toward it at 10 miles per hour. Write an equation for the distance of the boat from the marina after t hours.

d ( t ) = 100 10 t

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Questions & Answers

what is the function of sine with respect of cosine , graphically
Karl Reply
tangent bruh
Steve
cosx.cos2x.cos4x.cos8x
Aashish Reply
sinx sin2x is linearly dependent
cr Reply
what is a reciprocal
Ajibola Reply
The reciprocal of a number is 1 divided by a number. eg the reciprocal of 10 is 1/10 which is 0.1
Shemmy
 Reciprocal is a pair of numbers that, when multiplied together, equal to 1. Example; the reciprocal of 3 is ⅓, because 3 multiplied by ⅓ is equal to 1
Jeza
each term in a sequence below is five times the previous term what is the eighth term in the sequence
Funmilola Reply
I don't understand how radicals works pls
Kenny Reply
How look for the general solution of a trig function
collins Reply
stock therom F=(x2+y2) i-2xy J jaha x=a y=o y=b
Saurabh Reply
sinx sin2x is linearly dependent
cr
root under 3-root under 2 by 5 y square
Himanshu Reply
The sum of the first n terms of a certain series is 2^n-1, Show that , this series is Geometric and Find the formula of the n^th
amani Reply
cosA\1+sinA=secA-tanA
Aasik Reply
Wrong question
Saad
why two x + seven is equal to nineteen.
Kingsley Reply
The numbers cannot be combined with the x
Othman
2x + 7 =19
humberto
2x +7=19. 2x=19 - 7 2x=12 x=6
Yvonne
because x is 6
SAIDI
what is the best practice that will address the issue on this topic? anyone who can help me. i'm working on my action research.
Melanie Reply
simplify each radical by removing as many factors as possible (a) √75
Jason Reply
how is infinity bidder from undefined?
Karl Reply

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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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