How do you write the equation of the line that has contains the point (5, -4) and has a slope of 5?

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Answer 1 · 2017-01-10T15:02:09

#(y + color(red)(4)) = color(blue)(5)(x - color(red)(5))#

or

#y = color(blue)(5)x - 29#

We can use the point-slope formula to determine the equation of the line in this problem.

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 and point from the problem gives:

#(y - color(red)(-4)) = color(blue)(5)(x - color(red)(5))#

#(y + color(red)(4)) = color(blue)(5)(x - color(red)(5))#

We can put this in the more familiar slope-intercept form by solving for #y#:

#y + color(red)(4) = color(blue)(5)x - (color(blue)(5) xx color(red)(5))#

#y + color(red)(4) = color(blue)(5)x - 25#

#y + color(red)(4) - 4 = color(blue)(5)x - 25 - 4#

#y + 0 = color(blue)(5)x - 29#

#y = color(blue)(5)x - 29#