# How do you write an equation of the line that passes through the given (3,4); m=-4?

Nov 15, 2016

$y = - 4 x + 16$

#### Explanation:

You have 2 choices for the equation of a straight line:

• Substitute into the "point-slope" form $y - {y}_{1} = m \left(x - {x}_{1}\right)$ which involves one one substitution and some simplifying.

• Substitute into the "slope-intercept" form to find $c$ first. This involves two substitutions.

My choice is the first option. You have $m = - 4 \mathmr{and} \left(3 , 4\right)$

$y - {y}_{1} = m \left(x - {x}_{1}\right) \text{ } \leftarrow$ leave $x \mathmr{and} y$
$\textcolor{w h i t e}{\times} \downarrow \textcolor{w h i t e}{\times} \downarrow \textcolor{w h i t e}{\times . x} \downarrow$

$y \textcolor{b l u e}{- 4} = - 4 \left(x - 3\right)$

$y = - 4 x + 12 \textcolor{b l u e}{+ 4}$

$y = - 4 x + 16$