How do you write the equation in point slope form given (4, 0) and (2, 6)?

1 Answer
smendyka
Apr 2, 2017

See the entire solution process below:

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)(6) - color(blue)(0))/(color(red)(2) - color(blue)(4)) = 6/-2 = -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:

Solution 1) #(y - color(red)(0)) = color(blue)(-3)(x - color(red)(4))#

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

Solution 2) #(y - color(red)(6)) = color(blue)(-3)(x - color(red)(2))#

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