Chapter 5.6, Problem 4P

Write an equation of the line that passes through the given point and is parallel to the graph of the given equation.

$(6,2)$

$;y=\frac{2}{3}x+19$

To determine

To find: The equation of the line that passes through $(6,2)$ and is parallel to $y=\frac{2}{3}x+19$ .

Answer to Problem 4P

The equation of the required line is $y=\frac{2}{3}x-2$ .

Explanation of Solution

Given information:

  $(6,2);y=\frac{2}{3}x+19$

The slope of the line $y=\frac{2}{3}x+19$ is $\frac{2}{3}$ .

Since the line is parallel to the line $y=\frac{2}{3}x+19$ , the slope of the line would be, the same, $\frac{2}{3}$ .

So using the point-slope form of a line, the equation of the line can be determined as follows:

  $\begin{array}{l}y-y_1=m(x-x_1)\\ \Rightarrow y-2=\frac{2}{3}(x-6)\\ \Rightarrow y-2=\frac{2}{3}x-4\\ \Rightarrow y=\frac{2}{3}x-2\end{array}$

Conclusion:

Therefore, the equation of the required line is $y=\frac{2}{3}x-2$ .