Consider the line $y=\frac{2}{9}x-6$.
Find the equation of the line that is perpendicular to this line and passes through the point $(4,6)$.
Find the equation of the line that is parallel to this line and passes through the point $(4,6)$.
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Equation of perpendicular line: $◻$
$$\text{ 믐 }◻=◻$$

Equation of parallel line:
$$\times 5$$

Step 1 ：The slope of the given line is $\frac{2}{9}$.

Step 2 ：The slope of a line perpendicular to this would be the negative reciprocal, which is $-\frac{9}{2}$.

Step 3 ：The slope of a line parallel to this would be the same as the original line, which is $\frac{2}{9}$.

Step 4 ：We can use the point-slope form of a line, $y-y_1=m(x-x_1)$, to find the equations of the lines. Here, $(x_1,y_1)=(4,6)$ is the point through which the lines pass.

Step 5 ：The equation of the line that is perpendicular to the given line and passes through the point $(4,6)$ is $\boxed{{\displaystyle 4.5x+y=24}}$.

Step 6 ：The equation of the line that is parallel to the given line and passes through the point $(4,6)$ is $\boxed{{\displaystyle 0.222x-y=-5.111}}$.