# What is the equation of the line with slope  m=-4  that passes through  (4,5) ?

May 11, 2018

$4 x + y - 21 = 0$

#### Explanation:

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$
where $\left({x}_{1} , {y}_{1}\right)$ is $\left(4 , 5\right)$

$\left(y - 5\right) = - 4 \left(x - 4\right)$
$y - 5 = - 4 x + 16$
$4 x + y - 21 = 0$

May 11, 2018

$y = - 4 x + 21$

#### Explanation:

$m = - 4$ is equivalent to the gradient by $y = m x + c$. The coordinates $\left(5 , 4\right)$ indicates that the point occurs when $x = 5$ and $y = 4$ and these are free variables that you can plug in for $x$ and $y$.

Using the format of $y = m x + c$ solve for $c$:

$y = m x + c$
$5 = - 4 \left(4\right) + c$
$5 = - 16 + c$
$5 + 16 = c$
$c = 21$

Therefore, the equation for the slope is:

$y = - 4 x + 21$

May 11, 2018

Equation of the line is $4 x + y = 21$

#### Explanation:

The equation of line passing through $\left({x}_{1} = 4 , {y}_{1} = 5\right)$ having

slope of $m = - 4$ is y-y_1=m(x-x_1) ;

$\therefore y - 5 = - 4 \left(x - 4\right) \mathmr{and} y - 5 = - 4 x + 16$ or

 4 x + y =21 ;

Equation of the line is  4 x + y =21 ;  [Ans]