Chapter 13, Problem 21CR

To determine

To graph: The point of intersection of the two given lines.

Answer to Problem 21CR

The point of intersection of the two given lines is $\left(2,1\right)$ .

Explanation of Solution

Given information: The given equations of line are $y=2x-3$ and $x+2y=4$ .

Graph:

To find the coordinates of the lines, consider the expression of given equation:

  $y=2x-3$

Substitute $0$ for $x$ in the above expression.

  $\begin{array}{c}y=2\left(0\right)-3\\ =-3\end{array}$

Therefore, first coordinate of the line is $\left(0,-3\right)$ .

To determine second coordinate, substitute $1.5$ for $x$ in the above expression.

  $\begin{array}{c}y=2\left(1.5\right)-3\\ =0\end{array}$

Therefore, second coordinate of the line is $\left(1.5,0\right)$ .

To determine third coordinate, substitute $2$ for $x$ in the above expression.

  $\begin{array}{c}y=2\left(2\right)-3\\ =1\end{array}$

Therefore, third coordinate of the line is $\left(2,1\right)$ .

To find the coordinates of the lines, consider the expression of given equation:

  $\begin{array}{c}x+2y=4\\ 2y=-x+4\\ y=\frac{-x}{2}+2\end{array}$

Substitute $0$ for $x$ in the above expression.

  $\begin{array}{c}y=-\frac{0}{2}+2\\ =2\end{array}$

Therefore, first coordinate of the line is $\left(0,2\right)$ .

To determine second coordinate, substitute $2$ for $x$ in the above expression.

  $\begin{array}{c}y=-\frac{2}{2}+2\\ =-1+2\\ =1\end{array}$

Therefore, second coordinate of the line is $\left(2,1\right)$ .

To determine third coordinate, substitute $4$ for $x$ in the above expression.

  $\begin{array}{c}y=-\frac{4}{2}+2\\ =-2+2\\ =0\end{array}$

Therefore, third coordinate of the line is $\left(4,0\right)$ .

Plot and connect the ordered pair of the equation of line $x+2y=4$ are $\left(0,2\right)$ , $\left(2,1\right)$ and $\left(4,0\right)$ and coordinates of the equation of line $y=2x-3$ through which it is passing are $\left(0,-3\right)$ , $\left(1.5,0\right)$ and $\left(2,1\right)$ on the coordinate graph as shown below:

  

Therefore, the point of intersection of the two given lines from the above graph is $\left(2,1\right)$ .