Chapter 5.6, Problem 1P

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

$(3,2);y=3x-2$

To determine

To find: The equation of the line that passes through $(3,2)$ and is parallel to $y=3x-2$ .

Answer to Problem 1P

The equation of the required line is $y=3x-7$ .

Explanation of Solution

Given information:

  $(3,2);y=3x-2$

The slope of the line $y=3x-2$ is $3$ .

Since the line is parallel to the line $y=3x-2$ , the slope of the line would be, the same, 3.

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

  $\begin{array}{l}y-y_1=m(x-x_1)\\ \Rightarrow y-2=3(x-3)\\ \Rightarrow y-2=3x-9\\ \Rightarrow y=3x-7\end{array}$

Conclusion:

Therefore, the equation of the required line is $y=3x-7$ .