Question

Find an equation of the line through the points of intersection.

y= x^2-4x +3
y= -x^2 +2x +3

how do I find this line???

Answer 1

i explained this earlier
equate these two equations and solve for x:
x^2-4x +3 = -x^2 +2x +3
2x^2 - 6x = 0
2x (x - 3) = 0
x = 0 or x = 3
y coordinates of these points are 3 and 0 respectively

so line passes through the points (0,3) and (3,0)
slope of the line is -1
y-3 = -1(x-0)
y + x = 3
is the equation you require

Answer 2

y=-x + 3
You can achieve this by finding the points of intersection, by equation the two equations for y. you'll find the there are two points of intersection, at (0,3) and (3,0). since you now have two points on the line you can find its gradient m=(3-0)/(0-3) = -1
We have the gradient and a point on the line so we can find its equation using:
\[y-y _{1}=m(x-x _{1})\]
y-0=-(x+3)
y=-x +3