Chapter 1.5, Problem 9CFU

To determine

To find: the standard form of line equation.

Answer to Problem 9CFU

  $-5x+y+16=0$

Explanation of Solution

Given information:

A line passes through $A\left(5,9\right)$ and parallel to $y=5x-9$ .

Calculation:

Slope of two parallel lines are always equal.

A line parallel to line of equation, $y=5x-9$ . So, the slope (m) is 5.

Put the coordinates and slope value in the slope intercept equation and solve as follows:

  $\begin{array}{c}y=mx+b\\ 9=\left(5\right)5+b\\ 9=25+b\\ b=9-25\\ b=-16\end{array}$

Equations for converting the slope and y-intercept into standard form as follows:

  $\begin{array}{l}m=-\frac{A}{B}\text{ and }b=-\frac{C}{B}\\ 5=-\frac{A}{B}\text{ and }-16=-\frac{C}{B}\left[\text{Put values of }m\text{ and }b\right]\\ 5=-\frac{A}{1}\text{ and }-16=-\frac{C}{1}\left[\text{Let }B=1\right]\\ -5=A\text{ and 16}=C\left[\text{Simplify}\right]\end{array}$

Substitute the value of $A,B\text{ and }C$ in the standard form of line as shown below.

  $\begin{array}{l}Ax+By+C=0\\ -5x+1y+16=0\\ -5x+y+16=0\end{array}$

Thus, the standard form of line is $-5x+y+16=0$ .