1. Home
  2. Elementary algebra
  3. Graphs
  4. Find the equation of a line

4.6 Find the equation of a line  (Page 3/7)

<< Chapter < Page
  Elementary algebra     Page 3 / 7
Chapter >> Page >

Find an equation of a line given two points

Find an equation of a line that contains the points ( 5 , 4 ) and ( 3 , 6 ) . Write the equation in slope–intercept form.

This figure is a table that has three columns and four rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains further written instructions. The third column contains math. In the first row of the table, the first cell on the left reads: “Step 1. Find the slope using the given points.” The text in the second cell reads: “To use the point-slope form, we first find the slope.” The third cell contains the slope of a line formula: m equals y superscript 2 minus y superscript 1 divided by x superscript 2 minus x superscript 1. Below this is m equals 6 minus 4 divided by 3 minus 5. Below this is m equals 2 divided by negative 2. Below this is m equals negative 1. In the second row, the first cell reads: “Step 2. Choose one point.” The second cell reads: “Choose either point.” The third cell contains the ordered pair (5, 4) with a superscript x subscript 1 over 5 and a superscript y subscript 1 over 4. In the third row, the first cell reads: “Step 3. Substitute the values into the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses.” The top line of the second cell is left blank. The third cell contains the point-slope form, y minus y subscript 1 equals m times x minus x subscript 1 in parentheses. Below this is the point-slope form with 5 substituted for x subscript 1, 4 substituted for y subscript 1, and negative 1 substituted for m: y minus 4 equals negative 1 times x minus 5 in parentheses. Below this is y minus 4 equals negative x plus 5. In the fourth row, the first cell reads: “Step 4. Write the equation in slope-intercept form.” The second cell is blank. The third cell contains y equals negative x plus 9.


Use the point ( 3 , 6 ) and see that you get the same equation.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Find an equation of a line containing the points ( 3 , 1 ) and ( 5 , 6 ) .

y = 5 2 x − 13 2

Got questions? Get instant answers now!

Find an equation of a line containing the points ( 1 , 4 ) and ( 6 , 2 ) .

y = − 2 5 x + 22 5

Got questions? Get instant answers now!

Find an equation of a line given two points.

  1. Find the slope using the given points.
  2. Choose one point.
  3. Substitute the values into the point-slope form, y − y 1 = m ( x − x 1 ) .
  4. Write the equation in slope–intercept form.

Find an equation of a line that contains the points ( −3 , −1 ) and ( 2 , −2 ) . Write the equation in slope–intercept form.

Solution

Since we have two points, we will find an equation of the line using the point–slope form. The first step will be to find the slope.

Find the slope of the line through (−3, −1) and (2, −2). .
.
.
.
Choose either point. .
Substitute the values into y − y 1 = m ( x − x 1 ) . .
.
.
Write in slope–intercept form. .

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Find an equation of a line containing the points ( −2 , −4 ) and ( 1 , −3 ) .

y = 1 3 x − 10 3

Got questions? Get instant answers now!

Find an equation of a line containing the points ( −4 , −3 ) and ( 1 , −5 ) .

y = − 2 5 x − 23 5

Got questions? Get instant answers now!

Find an equation of a line that contains the points ( −2 , 4 ) and ( −2 , −3 ) . Write the equation in slope–intercept form.

Again, the first step will be to find the slope.

Find the slope of the line through ( −2 , 4 ) and ( −2 , −3 ) . m = y 2 − y 1 x 2 − x 1 m = −3 − 4 −2 − ( −2 ) m = −7 0 The slope is undefined.

This tells us it is a vertical line. Both of our points have an x -coordinate of −2 . So our equation of the line is x = −2 . Since there is no y , we cannot write it in slope–intercept form.

You may want to sketch a graph using the two given points. Does the graph agree with our conclusion that this is a vertical line?

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Find an equation of a line containing the points ( 5 , 1 ) and ( 5 , −4 ) .

x = 5

Got questions? Get instant answers now!

Find an equaion of a line containing the points ( −4 , 4 ) and ( −4 , 3 ) .

x = −4

Got questions? Get instant answers now!

We have seen that we can use either the slope–intercept form or the point–slope form to find an equation of a line. Which form we use will depend on the information we are given. This is summarized in [link] .

To Write an Equation of a Line
If given: Use: Form:
Slope and y -intercept slope–intercept y = m x + b
Slope and a point point–slope y − y 1 = m ( x − x 1 )
Two points point–slope y − y 1 = m ( x − x 1 )

Find an equation of a line parallel to a given line

Suppose we need to find an equation of a line that passes through a specific point and is parallel to a given line. We can use the fact that parallel lines have the same slope. So we will have a point and the slope—just what we need to use the point–slope equation.

First let’s look at this graphically.

The graph shows the graph of y = 2 x − 3 . We want to graph a line parallel to this line and passing through the point ( −2 , 1 ) .

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 7 to 7. The line whose equation is y equals 2x minus 3 intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (3 halves, 0). Elsewhere on the graph, the point (negative 2, 1) is plotted.

We know that parallel lines have the same slope. So the second line will have the same slope as y = 2 x − 3 . That slope is m ∥ = 2 . We’ll use the notation m ∥ to represent the slope of a line parallel to a line with slope m . (Notice that the subscript ∥ looks like two parallel lines.)

The second line will pass through ( −2 , 1 ) and have m = 2 . To graph the line, we start at ( −2 , 1 ) and count out the rise and run. With m = 2 (or m = 2 1 ), we count out the rise 2 and the run 1. We draw the line.

Questions & Answers

what does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
Wekolamo Reply
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Manix Reply
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
good👍
Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
Heidi Reply
treat them normal, if they want help then give them. that will make everyone happy
Saurabh
What are the treatment for autism?
Magret Reply
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities. before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue.. sometimes due to these physical problems..the diagnosis may be misdiagnosed. treatment for autism. well it depends on the severity. since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision. play therapy. speech therapy. Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game. string and beads game. the more you interact with the child the more effective
Jharna
results you'll get.. please consult a therapist to know what suits best on your child. and last as a parent. I know sometimes it's overwhelming to guide a special kid. but trust the process and be strong and patient as a parent.
Jharna
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 1

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask