# What is the equations of a line that is parallel to y = -3x + 6 and contains the point (-3,-5)?

Jun 21, 2018

$y = - 3 x - 14$

#### Explanation:

Any line parallel to $y = - 3 x + 6$
will be in the form $y = - 3 x + c$ for some constant $c$

If $\left(x , y\right) = \left(- 3 , - 5\right)$ is a solution to such an equation, then replacing $y$ with $\left(- 5\right)$ and $x$ with $\left(- 3\right)$ gives
$- 5 = \left(- 3\right) \cdot \left(- 3\right) + c$

$\rightarrow - 5 = 9 + c$

$\rightarrow c = - 14$

So the desired parallel line would have the equation
$y = - 3 x - 14$

Jun 21, 2018

The equation of the line parallel to $y = - 3 x + 6$ that passes through the point $\left(- 3 , - 5\right)$ is:

$y = - 3 x - 14$

#### Explanation:

The line $y = - 3 x + 6$ is already in 'slope-intercept' form, so we can just read off the slope (gradient) as being $- 3$.

We want a line with a gradient of $- 3$ (because that's what 'parallel' means - having the same gradient) that passes through the point $\left(- 3 , - 5\right)$.

Take the form $y = m x + c$ and substitute in the 3 things we already know: the slope, one value of $x$ and one value of $y$:

$- 5 = \left(- 3\right) \left(- 3\right) + c$

$c$ is the y-intercept of the line: the $y$ coordinate of the point at which it cuts the $y$ axis (which is the line $x = 0$).

$- 5 = 9 + c$

Subtract $9$ from both sides:

$- 14 = c$

That means the equation of the line is $y = - 3 x - 14$