How do you write the point slope form of the equation given (3,4) and (-7,4)?

1 Answer
smendyka
Jun 11, 2017

See a solution process below:

Explanation:

Because both of the #y# values are the same this is, by definition a vertical line. A vertical line has the same #y# value for each and every value of #x#.

The slope of a vertical line, also by definition is #0#:

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.

We can use this slope and the values from either of the points in the problem to write the point-slope formula as:

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

Or

#(y - color(red)(4)) = color(blue)(0)(x - color(red)(-7))#

#(y - color(red)(4)) = color(blue)(0)(x + color(red)(7))#

We can also, write this equation in the generic form of:

#(y - color(red)(4)) = color(blue)(0)(x + color(green)(a))#

Where #color(green)(a)# is an value you want to select.

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