MYTUTOR SUBJECT ANSWERS

681 views

How do I find the intersection of a line and a curve?

Say you are given the equations of both a line and a curve, for example y=x2+8x-1 and y=3x-7, and asked to find where these two intersect. This just means where the two lines would cross or touch if drawn on the same graph.

To find these points you simply have to equate the equations of the two lines, where they equal eachother must be the points of intersection.

For this example this would mean x2+8x-1=3x-7

Collecting like terms leads to x2+5x+6=0

And from then this is a simple case of solving the quadratic. This expression factorises to (x+2)(x+3)=0 which implies either x=-2 or x=-3. To find the corresponding y coordinates for each point simply input these x values one at a time into either one of the original equations.

For x=-2, we get y=3(-2)-7=-13 so the point is (-2,-13)

For x=-3, we get y=3(-3)-7=-16 so the point is (-3,-16)

Both of these are valid intersection points for the line and curve given. 

Lauren M. A Level Maths tutor, GCSE Maths tutor, A Level Further Math...

1 year ago

Answered by Lauren, a GCSE Maths tutor with MyTutor


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

571 SUBJECT SPECIALISTS

£18 /hr

Dan W.

Degree: Economics and Accounting (Bachelors) - Bristol University

Subjects offered:Maths, Economics

Maths
Economics

“I achieved top grades whilst juggling cricket at a high level. I’ve tutored for Young Einstein Tuition & been a Peer Mentor to those facing personal issues”

£18 /hr

Georgia H.

Degree: Politics and International Relations (Bachelors) - Cambridge University

Subjects offered:Maths, Politics+ 3 more

Maths
Politics
Government and Politics
English
-Oxbridge Preparation-

“I'm an enthusiastic and passionate student with a real interest in helping others achieve their aims and increasing their enjoyment of their subjects!”

MyTutor guarantee

PremiumTimothy N. A Level Design & Technology tutor, GCSE Design & Technolog...
£36 /hr

Timothy N.

Degree: Architecture and Environmental Engineering (Masters) - Nottingham University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Design & Technology
-Personal Statements-

“Hi there, I have a passion for helping students achieve, and believe that with my 200+ hours of experience, we will be able to surpass the grades you want!”

About the author

Lauren M.

Currently unavailable: for regular students

Degree: Physics (Masters) - Warwick University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
-Personal Statements-

“About Me: I am a physics student at Warwick University, although for the first 2 years of my degree I studied joint honours Maths and Physics. I have always had a real passion for the sciences and hope that my tutorials can inspire yo...”

MyTutor guarantee

|  1 completed tutorial

You may also like...

Other GCSE Maths questions

Find the coordinates where the curve y=x^2+6x+5 crosses the x-axis.

Could you explain ratios to me?

How do I expand double brackets?

Please factorise fully: 2a^2 + 6a

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

mtw:mercury1:status:ok