How do you write the point slope form of the equation given (4,-4) parallel to #y=-x-4#?

1 Answer
Mar 5, 2017

Answer:

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

Explanation:

The equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

Therefore: #y = color(red)(-1)x - color(blue)(4)# and #color(red)(m = -1)#. A parallel line will have the same slope, or #m = -1#

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 slope we derived and the point from the problem gives:

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

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