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...

2 years ago

Answered by Chris, a GCSE Maths tutor with MyTutor

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


£18 /hr

Anezka E.

Degree: Mathematics (Bachelors) - Kings, London University

Subjects offered: Maths


“About me: I'm hopefully about to start my second year at King's College London. I've thouroughly enjoyed studying maths for many years now and would love to help out a maths lover or hater and hopefully convert the latter into the for...”

MyTutor guarantee

£18 /hr

Visitation L.

Degree: Biomedical sciences (Bachelors) - Durham University

Subjects offered: Maths, Biology


“Hi, I am Visitation, a second year Biomedical scientist at Durham. Science and Maths are such fascinating subjects and I would like to share my passion and help you through my tutorials!”

£18 /hr

Jessica K.

Degree: History (Bachelors) - Manchester University

Subjects offered: Maths


“Hi! I'm Jessica, and I am studing History at the University of Manchester. My interests in maths have developed following my studies at both GCSE and A-level. Over the years of these studies I attended many tutoring sessions to help d...”

MyTutor guarantee

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

differentiate x^3(1+x)^5 with respect for x

Lisa, Max and Punita share £240 in the ratio 3 : 4 : 8 How much more money than Lisa does Punita get?

How do i solve the quadratic x^2 + 5x + 6 = 0 ?

Which has greater area? A parallelogram with base length 10cm and perpendicular height 6cm, or a circle of diameter 8cm.

View GCSE Maths tutors


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