How do you write the equation in point slope form given (5,6) and (10, 9)?

1 Answer
smendyka
Feb 16, 2017

#(y - color(red)(6)) = color(blue)(3/5)(x - color(red)(5))#

Or

#(y - color(red)(9)) = color(blue)(3/5)(x - color(red)(10))#

Explanation:

First, we need to determine the slope of the line. 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)(9) - color(blue)(6))/(color(red)(10) - color(blue)(5)) = 3/5#

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 calculated and the first point gives:

#(y - color(red)(6)) = color(blue)(3/5)(x - color(red)(5))#

We can also substitute the slope we calculated and the second point giving:

#(y - color(red)(9)) = color(blue)(3/5)(x - color(red)(10))#

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