What is the equation of the line with slope $m = - 5$ $m= -5$ that passes through $(- 1, - 3)$ $(-1,-3)$ ?

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Answer 1 · 2018-04-24T01:00:54

$y = - 5 x - 8$ $y =-5x-8$

Since we are provided the slope and a point on the line we can use the equation for point slope form of the equation of a line.

$y - y_{1} = m (x - x_{1})$ $y-y_1 =m(x-x_1)$

Where $m =$ $m=$ slope and the point is $(x_{1}, y_{1})$ $(x_1,y_1)$

For this situation $m = - 5$ $m=-5$ and a point of $(- 1, - 3)$ $(-1,-3)$

$m = - 5$ $m=-5$
$x_{1} = - 1$ $x_1=-1$
$y_{1} = - 3$ $y_1=-3$

$y - y_{1} = m (x - x_{1})$ $y-y_1 =m(x-x_1)$

Plug in the values
$y - (- 3) = - 5 (x - (- 1))$ $y-(-3) =-5(x-(-1))$

Simplify the signs
$y + 3 = - 5 (x + 1)$ $y+3 =-5(x+1)$

Use distributive property to eliminate the parenthesis
$y + 3 = - 5 x - 5$ $y+3 =-5x-5$

Use the additive inverse to isolate the $y$ $y$ value
$y cancel(+3) cancel(-3) =-5x-5-3$

Simplify the common terms
$y =-5x-8$

What is the equation of the line with slope m= -5 m=−5 m= -5 that passes through (-1,-3) (−1,−3) (-1,-3) ?