Chapter 12.7, Problem 10MRE

To determine

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

  $\left(-1,-1\right)and\left(7,23\right)$

Answer to Problem 10MRE

The equation of the line in standard form is $3x-y=-2$

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:

  $\left(-1,-1\right),\left(7,23\right)$

Put the points in equation 2.

  $\begin{array}{l}\frac{y-\left(-1\right)}{23-\left(-1\right)}=\frac{x-\left(-1\right)}{7-\left(-1\right)}\\ \frac{y+1}{23+1}=\frac{x+1}{7+1}\end{array}$

  $\frac{y+1}{24}=\frac{x+1}{8}$

  $\frac{y+1}{3}=x+1$

Solve further,

  $3\left(x+1\right)=y+1$

  $3x+3=y+1$

  $3x-y=1-3$

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

  $3x-y=-2$