Chapter 9.8, Problem 31PPE

To determine

To determine the equation of line.

Answer to Problem 31PPE

The points of intersection are (0, 2) (2, 6)

Equation of line is $y=2x+2$

Explanation of Solution

Given information:

Given equations,

  $y=3x^2-4x+2$

First we shall find the points of intersection.

It is given that the line intersects the parabola when $x=0,x=2$

Hence using this we may find $y$ coordinates.

Now we put $x=0,x=2$ in the given equation to find point of intersection.

  $\begin{array}{l}y=3{\left(0\right)}^2-4\left(0\right)+2\\ y=2\\ y=3{\left(2\right)}^2-4\left(2\right)+2\\ y=6\end{array}$

Hence the points of intersection are (0, 2) (2, 6)

Now we know the equation of line with two cordinates given is $y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)$

Hence put values we get,

  $\begin{array}{l}y-2=\left(\frac{6-2}{2-0}\right)\left(x-0\right)\\ y-2=2x\\ y=2x+2\end{array}$