How do you write an equation in point slope form given (9,0) and (6,-1)?

1 Answer
smendyka
May 21, 2017

See a solution process below:

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)(-1) - color(blue)(0))/(color(red)(6) - color(blue)(9)) = (-1)/-3 = 1/3#

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 values from the first point in the problem gives:

#(y - color(red)(0)) = color(blue)(1/3)(x - color(red)(9))#

We can also substitute the slope we calculated and the values from the second point in the problem giving:

#(y - color(red)(-1)) = color(blue)(1/3)(x - color(red)(6))#

#(y + color(red)(1)) = color(blue)(1/3)(x - color(red)(6))#

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