Chapter 12.7, Problem 7MRE

To determine

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

  $\left(4,1\right),\left(0,-7\right)$

Answer to Problem 7MRE

The equation of the line in standard form is $2x-y=7$

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:

  $\left(4,1\right),\left(0,-7\right)$

Put the points in equation 2.

  $\frac{y-1}{-7-1}=\frac{x-4}{\begin{array}{l}0-4\end{array}}$

  $\frac{y-1}{-8}=\frac{x-4}{\begin{array}{l}-4\end{array}}$

Cancel negative at both sides:

  $\frac{y-1}{8}=\frac{x-4}{4}$

  $\frac{y-1}{2}=x-4$

  $2\left(x-4\right)=y-1$

  $2x-8=y-1$

  $2x-y=-1+8$

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

  $2x-y=7$