How do you write the point slope form of the equation given (-2,4) parallel to #y=-5/2x+5#?

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Answer 1 · 2017-06-03T23:05:16

See a solution process below:

The equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

#y = color(red)(-5/2)x + color(blue)(5)#

Therefore the slope of this line is: #color(red)(m = -5/2)#

Because the line we are looking for is parallel to this line by definition it will have the same slope.

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 determined and the values from the point in the problem gives:

#(y - color(red)(4)) = color(blue)(-5/2)(x - color(red)(-2))#

#(y - color(red)(4)) = color(blue)(-5/2)(x + color(red)(2))#