Chapter 5.5, Problem 31P

Find the $x$- and $y$-intercepts of the line that passes through the given points.

$(1,1),(-5,7)$

To determine

To find: The equation of the line that passes through the points: $(1,1),(-5,7)$ .

Answer to Problem 31P

The intercepts of the line are:

x -intercept: $a=2$

y -intercept: $b=2$

Explanation of Solution

Given information:

The points are $(1,1),(-5,7)$ .

Formula used:

The equation of a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given as

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

The equation of a line in intercepts form is

  $\frac{x}{a}+\frac{y}{b}=1$

Where a is the x -intercept and b is the y -intercept.

Using the given points $(x_1,y_1)=(1,1)$ and $(x_2,y_2)=(-5,7)$ , the equation of the line is

  $\begin{array}{l}y-1=\frac{7-1}{-5-1}(x-1)\\ \Rightarrow y-1=\frac{6}{-6}(x-1)=-1(x-1)\\ \Rightarrow y-1=-x+1\\ \Rightarrow x+y=2\\ \Rightarrow \frac{x}{2}+\frac{y}{2}=1\end{array}$

Now, the above finding equation is in the intercepts form.

Conclusion:

Therefore, the intercepts of the line are:

x -intercept: $a=2$

y -intercept: $b=2$