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 - color(red)(4)) = color(blue)(-1)(x + color(red)(1))#

Or

#y = -x + 3#

The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#

Where #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#