Question

Find an equation of the line perpendicular to $3x-2y=7$that contains the point (1, 5).

Short answer

The equation of the line is$y=-\frac{2}{3}x+\frac{17}{3}$

Step-by-step solution

Given information

We are given an equation$3x-2y=7$

Find the slope of the perpendicular line

First we find the slope of given line

$$\begin{gathered} 3x-2y=7 \\ 2y=3x-7 \\ y=\frac{3}{2}x-\frac{7}{2} \end{gathered}$$

Hence the slope of line is $\frac{3}{2}$

Hence the slope of perpendicular line is$-\frac{2}{3}$

Find y-intercept

The line passes through the point $(1,5)$

We get,

$$\begin{gathered} y=-\frac{2}{3}x+c \\ 5=-\frac{2}{3}+c \\ c=\frac{17}{3} \end{gathered}$$

Hence the equation of the perpendicular line$y=-\frac{2}{3}x+\frac{17}{3}$

Conclusion

The equation of the line is$y=-\frac{2}{3}x+\frac{17}{3}$