Chapter 12.7, Problem 11MRE

To determine

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

  $\left(0,-4\right)and\left(-12,-6\right)$

Answer to Problem 11MRE

The equation of the line in standard form is $x-6y=24$

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:

  $\left(0,-4\right)\left(-12,-6\right)$

Put the points in equation 2.

  $\begin{array}{l}\frac{y-\left(-4\right)}{-6-\left(-4\right)}=\frac{x-0}{-12-0}\\ \frac{y+4}{-6+4}=\frac{x}{-12}\end{array}$

  $\frac{y+4}{-2}=\frac{x}{-12}$

Cancel negative at both sides:

  $y+4=\frac{x}{6}$

  $6\left(y+4\right)=x$

  $6y+24=x$

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

  $x-6y=24$