Chapter 1.7, Problem 32E

To determine

To find: standard form of line equation at given condition.

Answer to Problem 32E

  $2x-y-6=0$

Explanation of Solution

Given information:

The line passes through $\left(4,2\right)$ and it is parallel to line equation $y=2x-4$ .

Calculation:

Let the line $l$ be parallel to $y=2x-4$ . So, the slope of both the lines will be equal.

Compare the given line equation with the slope intercept form as shown below.

  $\begin{array}{l}y=mx+b\\ y=2x-4\\ \therefore m=2\end{array}$

Put the point coordinates and value of m in the slope intercept formula and evaluate the y- intercept as follows:

  $\begin{array}{c}y=mx+b\\ 2=2\left(4\right)+b\\ 2=8+b\\ b=2-8\\ =-6\end{array}$

Substitute the value of m and b in the slope intercept formula to evaluate the line equation of l as follows:

  $\begin{array}{l}y=mx+b\\ y=2x-6\\ 2x-y-6=0\left[\text{Rearranging in the standard form }Ax+By-C=0\right]\end{array}$

Thus, the standard form of line equation is $2x-y-6=0$ .