Chapter 12.7, Problem 9MRE

To determine

To Calculate: An equation, in standard form, of the line passing through the given points.

  $\left(4,3\right)and\left(-4,7\right)$

Answer to Problem 9MRE

The equation of the line is the standard form is $x+2y=8$

Explanation of Solution

Given information:

As we know equation of line in standard form is $ax+by=c$.............(1)

And the equation of line passing through two points is represent as

  $\frac{y-y_1^{}}{y2-y_1^{}}=\frac{x-x_1^{}}{x_2^{}-x_1^{}}$............. (2)

where $\left(x_{1,}^{}{y}_1^{}\right)$ and $\left(x_{2,}^{}{y}_2^{}\right)$ are the points through which line is passing.

Given points are:

  $\left(4,3\right)and\left(-4,7\right)$

Put the points in equation 2.

  $\begin{array}{l}\frac{y-3}{7-7}=\frac{x-4}{-4-4}\\ \frac{y-3}{4}=\frac{x-4}{-8}\end{array}$

  $y-3=\frac{x-2}{-2}$

  $-2\left(y-3\right)=x-2$

Solve further,

  $-2y+6=x-2$

  $-2y=x-2-6$

  $-$$2y-x=-8$

  $-\left(x+2y\right)=-8$

So the equation of the line in standard form is given below which is in the same form as equation 1.

  $x+2y=8$