How do I find the equation of a line connecting points a(p,q) and b(r,s)?

First we need to find the gradient of the line connecting points a and b:
gradient m = (change in y)/(change in x) = (q - s)/(p -r)

Now we use the following equation:

y - y1 = m(x - x1)

substituting suitable values for (x1, y1) (can be points a or b but we'll use point a this time) and m (calculated above):

Using point a:

y - q = [(q-s)/(p-r)](x - p)

and so the equation in the form y = f(x) is:
y = [(q-s)/(p-r)]x + [(q-s)/(p-r)](-p) + q

Chris W. A Level Maths tutor, GCSE Maths tutor, A Level Further Mathe...

3 years ago

Answered by Chris, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£30 /hr

Ayusha A.

Degree: BEng electrical and electronics engineering (Bachelors) - Newcastle University

Subjects offered:Maths, Physics+ 1 more

Further Mathematics

“About me: I am a final year Electrical and Electronic Engineering student at Newcastle University. I took Mathematics, Further Mathematics, Chemistry and Physics as my A-level subjects. I did peer mentoring in university and also have...”

£22 /hr

Haider M.

Degree: Medicine (Bachelors) - Exeter University

Subjects offered:Maths, Physics+ 7 more

Extended Project Qualification
.BMAT (BioMedical Admissions)
-Personal Statements-
-Medical School Preparation-

“A bit about me I am currently in my 2nd year of medical school at the University of Exeter. I really enjoy learning about science, especially the science of health disease, and would love nothing more than to pass down this knowledge ...”

£30 /hr

Szymon K.

Degree: Mechanical Engineering (Masters) - Manchester University

Subjects offered:Maths, Physics+ 1 more

Further Mathematics

“About me: I am a student pursuing my degree in Mechanical Engineering at the University of Manchester. Ever since I can remember I have always been passionate about passing my knowledge to others. As a tutor I taught people of differen...”

About the author

Chris W.

Currently unavailable:

Degree: Mathematics (Bachelors) - Durham University

Subjects offered:Maths, Science+ 5 more

Further Mathematics
-Personal Statements-

“Hi! I'm Chris, a maths undergraduate at Durham University. I achieved 4 A* at A-Level and on track for a First at university. ”

You may also like...

Other GCSE Maths questions

Rectangle A has a length of 3y cm and a width of 2x cm. Rectangle B has a length of (y + 4)cm and a width of (x + 6)cm. Rectangle A has a perimeter of 94cm and Rectangle B has a perimeter of 56cm. Solve x and y and calculate the areas of each rectangle.

Solve x² + x -12

How do signs change in an inequality?

Expand and simplify 3(2x + 5) – 2(x – 4)

View GCSE Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss