# Question #8a759

##### 1 Answer
Apr 19, 2017

a. $y = - 2$
b. $y = 2 x - 3$
c. $y = 5$

#### Explanation:

For a., a horizontal line means that the line has a zero slope and thus the equation for this line is $y = - 2$

For b., you must use the point-slope formula: $y - {y}_{1} = m \left(x - {x}_{1}\right)$
Since the line must be parallel to the line $2 x + 3$, our slope (or $m$) has to be the same as the equation just mentioned: $2$. In addition we are given the point $\left(5 , 7\right) \to \left({x}_{1} , {y}_{1}\right)$

We can now substitute for the point-slope formula:

$y - 7 = 2 \left(x - 5\right)$

$y - 7 = 2 x - 10$

We can rewrite the equation in $y = m x + b$ form by adding $7$ to both sides.

$y \cancel{- 7 + 7} = 2 x - 10 + 7$

$y = 2 x - 3$

For c.

First we find the slope using: $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

We know that:
$\left(- 3 , 5\right) \to \left({x}_{1} , {y}_{1}\right)$
$\left(2 , 5\right) \to \left({x}_{2} , {y}_{2}\right)$

Thus:

$m = \frac{5 - 5}{2 - \left(- 3\right)} = \frac{0}{5} = 0$

$m = 0$

Now we can use the point slope formula to find the equation for this line using our newly found $m$ and any of the two points given. I will use $\left(2 , 5\right)$

$y - 5 = 0 \left(x - 2\right)$

$y - 5 = 0$

In $y = m x + b$ form, we add $5$ to both sides

$y \cancel{- 5 + 5} = 0 + 5$

$y = 5$