Three less than five times a number is the same as two more than twice that number.

Let the number be $\displaystyle n$.

"Three less than five times a number" translates into $\displaystyle 5n-3$.

"Is the same as" means equal to or "$\displaystyle =$".

"Two more than twice that number" means $\displaystyle 2n+2$.

Putting these together gives:

$\displaystyle 5n-3 = 2n+2$

By changing the equation to slope intercept form we get the following:

$\displaystyle y = \frac{3}{2}x-5$

Hence the slope is

$\displaystyle m=\frac{3}{2}$

For a vertical line e.g. $\displaystyle x=-3$, $\displaystyle run=0$ and $\displaystyle \frac{rise}{0}=undefined$

This line does not intersect the $\displaystyle y-axis$ and hence there is no $\displaystyle y-intercept$.

Since the line passes through $\displaystyle \left ( -3,0 \right )$ hence the $\displaystyle x$-intercept $\displaystyle =-3$.

Here we use the point-slope formula of a line which is

$\displaystyle \left ( y-y_{1} \right )=m\left ( x-x_{1} \right )$

By plugging in $\displaystyle m$, $\displaystyle x_{1}$, and $\displaystyle y_{1}$ values we get the following:

$\displaystyle \left ( y-\left ( -2 \right ) \right ) = \frac{-3}{5}\left ( x-5 \right )$

which is equal to

$\displaystyle \left ( y+2 \right ) =\frac{-3}{5}\left ( x-5 \right )$

When the above is simplified we get:

$\displaystyle y = \frac{-3}{5}x +1$

Replacing $\displaystyle x$ with $\displaystyle -6$, one gets $\displaystyle y=9$ which tells us that $\displaystyle \left ( -6,7 \right )$ is not a solution.

Multiplying each term of the given equation by the denominator of the slope which is 5 one gets :

$\displaystyle 5y=-3x+10$ 

which can be written as

$\displaystyle 3x+5y=10$

The equation of line $\displaystyle a$ is

$\displaystyle y=3$

Hence 

$\displaystyle rise = 0$

and the

$\displaystyle slope=0$

The equation of a line parallel to the given line must be of the form:

$\displaystyle y = -3x + b$

Since the line passes through $\displaystyle \left ( 2,1 \right )$,

we can calculate $\displaystyle b$ by replacing $\displaystyle x$ with 2 and $\displaystyle y$ with 1 which gives us the following

$\displaystyle 1 = -3\left ( 2 \right ) + b$

Solving for $\displaystyle b$ gives us the following equation

$\displaystyle y = -3x + 7$

The slope of a line perpendicular to

$\displaystyle y = -3x - 3$

which has a slope of $\displaystyle -3$, is the negative reciprocal of $\displaystyle -3$.

Hence we get

$\displaystyle y = \frac{1}{3}x + b$

Replacing $\displaystyle x$ and $\displaystyle y$ with the given point we get

$\displaystyle 1 = \frac{1}{3}\left ( 2 \right ) + b$

Solving for $\displaystyle b$ we get

$\displaystyle y = \frac{1}{3}x+ \frac{1}{3}$

Any line perpendicular to $\displaystyle y = 3$,

which is a horizontal line, must be a vertical line.

Since it passes through the point $\displaystyle \left ( -2, 2 \right )$ and must be perpendicular to

$\displaystyle y = 3$

The equation must be

$\displaystyle x = -2$