How do you write the point slope form of the equation given (0,4) and (1,-4)?

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Answer 1 · 2017-01-18T20:28:58

#(y - color(red)(4)) = color(blue)(-8)(x - color(red)(0))#

Or

#(y + color(red)(4)) = color(blue)(-8)(x - color(red)(1))#

First, we need to determine the slope.

The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.

Substituting the values from the two points in the problem gives:

#m = (color(red)(-4) - color(blue)(4))/(color(red)(1) - color(blue)(0))#

#m = -8/1 = -8#

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.

Solution 1) Using the calculated slope and the values from the first point in the problem gives:

#(y - color(red)(4)) = color(blue)(-8)(x - color(red)(0))#

Solution 1) Using the calculated slope and the values from the second point in the problem gives:

#(y - color(red)(-4)) = color(blue)(-8)(x - color(red)(1))#

#(y + color(red)(4)) = color(blue)(-8)(x - color(red)(1))#