Question

A certain system of a linear and a quadratic equation has two solutions, (2,7) and (5,10). The quadratic equation is y = x^2 - 6x + 15. What is the linear equation?

Answer 1

@Owlcoffee

Answer 2

@kidrah69

Answer 3

@TheSmartOne

Answer 4

@NoelGreco

Answer 5

@zepdrix

Answer 6

Hey :)

Answer 7

So we're given the quadratic, and we need to find the linear function.
It will have the form, in slope-intercept form, of:\[\Large\rm y=mx+b\]

Answer 8

This system has two solutions, meaning, that BOTH equations will pass through the given points.

So our linear equation will pass through these two points.
We can use our slope formula to find the slope between these two points.
\[\Large\rm m=\frac{y_2-y_1}{x_2-x_1}\]
Remember how to do that? :)

Answer 9

live saver right here, I remember this!

Answer 10

So what do you get for your slope? :U

Answer 11

1?

Answer 12

Mmm ok good!\[\Large\rm y=mx+b\]\[\Large\rm y=1x+b\]\[\Large\rm y=x+b\]Now we just need to find the starting point, the y-intercept.
Plug one of those two given points into the function, and solve for b.

Answer 13

b = 5, so the equation is y = x + 5

Answer 14

Yayyy good job \c:/
Here is what it looks like graphed just in case you were curious.
https://www.desmos.com/calculator/mgzzovgxtx

Answer 15

Woops this link:
https://www.desmos.com/calculator/07lq6tizry

Answer 16

Just a website for graphing :) Kinda useful.

Answer 17

Thank you zepdrix! I'll see you around : D