Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GRE score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Your score will improve and your results will be more realistic
Is there something wrong with our timer?Let us know!
Are you planning to take the GRE in a few weeks but disappointed with your progress in your GRE prep? Target Test Prep has just the solution: LiveTeach, our powerful, LIVE online classes.
8 Dec 2023 18:00 1 hr Don’t have collateral for your study abroad loan? Unsecured loans are your answer! Join the webinar to understand benefits, find top lenders and more.
Attached pdf of this Article as SPOILER at the top! Happy learning!
Hi All,
I have recently uploaded a video on YouTube to discuss Equation of a Line in Detail:
Following is covered in the video
¤ Equation of a Line: Two Point Form ¤ Equation of a Line: Point and Slope Form ¤ Equation of a Line: Intercept Form ¤ Generic Equation of a line (Point and Intercept Form) ¤ Equation of Horizontal and Vertical Lines
Equation of a Line: Two Point Form
Let's say we have a line passing through two point A(\(x_1\),\(y_1\)) and B(\(x_2\),\(y_2\)). Let's take a point C (x,y) on the line and between A and B as shown below.
Attachment:
EL img-1.jpg [ 20.58 KiB | Viewed 396 times ]
Slope of the Part CA of the line = Slope of the part BA of the line = Slope of the line
Equation of a line in Point and Slope Form as y - \(y_1\) = m * (x - \(x_1\))
Equation of a Line: Intercept Form
Let's say we have a line which intercepts X-Axis at point A(a,0) and Y-Axis at point B(0,b), as shown below.
Attachment:
EL img-2.jpg [ 20.17 KiB | Viewed 416 times ]
Using, \(\frac{y - y_1}{x - x_1}\) = \(\frac{y_2 - y_1}{x_2 - x_1}\) we get
\(\frac{y - 0}{x - a}\) = \(\frac{b - 0}{0 - a}\) => ay = -bx + ab => bx + ay = ab
Dividing both the sides by ab we get
Equation of a line in Intercept Form as \(\frac{x}{a}\) + \(\frac{y}{b}\) = 1
Generic Equation of a line (Point and Intercept Form)
Let's say we have a line which intercepts Y-Axis at point B(0,b) and has a slope m, as shown below.
Attachment:
EL - generic equation.jpg [ 20.28 KiB | Viewed 418 times ]
Using, y - \(y_1\) = m * (x - \(x_1\)) and substituting the value of Point B we get
y - b = m * (x - 0)
Generic Equation of a line (Point and Intercept Form) as y = mx + b
where m is the slope of the line and B is the y intercept.
Equation of horizontal and vertical lines
Let's say we have a line parallel to X-Axis and intersecting Y-Axis at point B(0,b) and a line which is parallel to Y-Axis and intercepting the X-Axis at point A(a,0) as shown below
Attachment:
EL - Horizontal and parallel lines.jpg [ 21.02 KiB | Viewed 418 times ]
Equation of Horizontal Line
Now, all the points on this line will be at the same distance b from X-Axis and will have the y-coordinate as b
=> Equation of Horizontal line will be y = b [constant]
Equation of Vertical Line
Now, all the points on this line will be at the same distance a from Y-Axis and will have the x-coordinate as a
=> Equation of Vertical line will be x = a [constant]