How do you write the equation in point slope form given (4,0) and (0,5)?

1 Answer
smendyka
Mar 6, 2017

#(y - color(red)(0)) = color(blue)(-5/4)(x - color(red)(4))#

Or

#(y - color(red)(5)) = color(blue)(-5/4)(x - color(red)(0))#

Explanation:

First, we must 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 points in the problem gives:

#m = (color(red)(5) - color(blue)(0))/(color(red)(0) - color(blue)(4)) = 5/-4 = -5/4#

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 calculate and the first point from the problem gives:

#(y - color(red)(0)) = color(blue)(-5/4)(x - color(red)(4))#

We can also substitute the slope we calculate and the second point from the problem giving:

#(y - color(red)(5)) = color(blue)(-5/4)(x - color(red)(0))#

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