How do you write an equation of a line with point (-1,4), slope -1?

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Answer 1 · 2017-01-22T18:42:16

$(y - 4) = - 1 (x + 1)$ $(y - color(red)(4)) = color(blue)(-1)(x + color(red)(1))$

Or

$y = - x + 3$ $y = -x + 3$

The point-slope formula states: $(y - y_{1}) = m (x - x_{1})$ $(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))$

Where $m$ $color(blue)(m)$ is the slope and $color(red)(((x_1, y_1)))$ is a point the line passes through.

Substituting the values from the problem gives:

$(y - color(red)(4)) = color(blue)(-1)(x - color(red)(-1))$

$(y - color(red)(4)) = color(blue)(-1)(x + color(red)(1))$

We can transform this into the more familiar slope-intercept form by solving for $y$ :

$y - color(red)(4) = (color(blue)(-1) xx x) + (color(blue)(-1) xx color(red)(1))$

$y - color(red)(4) = -1x - 1$

$y - color(red)(4) + 4 = -x - 1 + 4$

$y - 0 = -x + 3$

$y = -x + 3$