Chapter 5.5, Problem 55PPE

To determine

x and y intercept of the line that passes through the points (-2, 8) and (4, 2)

Answer to Problem 55PPE

The x and y intercepts are $\left(6,0\right)\text{and }\left(0,6\right)$

Explanation of Solution

Given:

The given points are,

  $\begin{array}{l}\left(x_1,y_1\right)=\left(-2,8\right)\\ \left(x_2,y_2\right)=\left(4,2\right)\end{array}$

The equation of line from the two points given is,

  $\left(y-y_1\right)=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

On substituting the values

  $\begin{array}{l}\left(y-8\right)=\frac{2-8}{4-\left(-2\right)}\left(x-\left(-2\right)\right)\\ \Rightarrow \left(y-8\right)=-\left(x+2\right)\end{array}$

Now, for x intercept put y = 0

  $\begin{array}{l}\left(0-8\right)=-\left(x+2\right)\\ \Rightarrow x=-2+8\\ \Rightarrow x=6\end{array}$

And for y intercept put x = 0

  $\begin{array}{l}\left(y-8\right)=-\left(0+2\right)\\ \Rightarrow y=6\end{array}$

Therefore , the x and y intercepts are $\left(6,0\right)\text{and }\left(0,6\right)$