SOLUTION: How to find an equation of a line that is intercepting the two parabolas?

Question 234418: How to find an equation of a line that is intercepting the two parabolas?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
You find any point on one of the paraboles and you find any point on the other parabola and you create a line using those two points.

If the points are (x1,y1) and (x2,y2), then the equation of the line would be:

y = mx + b where:

m is the slope = (y2-y1)/(x2-x1)

b is the y-intercept.

To find b, replace y with y1, and replace x with x1 to get:

y1 = m*x1 + b and solve for b.

This is after you found m, of course.

Example:

m = 5
y1 = 6
x1 = 3

To find b, you replace m with 5, y with 6, x with 3, to get:

y = mx + b becomes:

6 = 5*3 + b and you solve for b.

The line will intersect both parabolas because it was created from a point on both parabolas.

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