Chapter 12.7, Problem 12MRE

To determine

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

  $\left(0,-10\right)and\left(13,-5\right)$

Answer to Problem 12MRE

The equation of the line is the standard form is $5x-13y=130$

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:

  $\left(0,-10\right)and\left(13,-5\right)$

Put the points in equation 2.

  $\begin{array}{l}\frac{x-0}{13-0}=\frac{y-\left(-10\right)}{-5-\left(-10\right)}\\ \frac{x}{13}=\frac{y+10}{-5+10}\end{array}$

  $\frac{x}{13}=\frac{y+10}{5}$

  $5x=13\left(y+10\right)$

  $5x=13y+130$

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

  $5x-13y=130$