893 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.

2 years ago

Answered by Lauren, a GCSE Maths tutor with MyTutor

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

#### 786 SUBJECT SPECIALISTS

£18 /hr

Degree: Psychology (Bachelors) - University College London University

Subjects offered:Maths, Psychology

Maths
Psychology

“Hi, I'm Emily! I'm an enthusiastic Psychology graduate offering tuition in both Psychology and Maths and willing to help give any advice I can!”

£30 /hr

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“2nd year Maths student at Warwick, after a few tutorials you'll see Maths isn't the scary, hard subject most people think it is - it's actually really fun!”

£22 /hr

Degree: Natural Sciences (Masters) - Durham University

Subjects offered:Maths, Spanish+ 3 more

Maths
Spanish
Physics
Further Mathematics
-Personal Statements-

“Enthusiastic student, studying Maths and Physics at Durham university: keen to work hard with students to improve their results.”

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

There are 200 students in Year 10 110 are boys. There are 250 students in Year 11 140 are boys. Which year has the greater proportion of boys? (Taken from Nov 2014 AQA Unit 2)

How should I approach my GCSE maths paper?

At what points does the line y = x +1 intersect the circle x^2 + y^2 + 18x + 20y + 81 = 0.

How do I solve a quadratic equation by completing the square?

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