How do you write an equation in point slope form given (3/2, -1/3), (-2/3, 4)?

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Answer 1 · 2017-06-12T02:49:07

#y+1/3 = -2(x-3/2)#

We are given the points #(color(limegreen)(3/2), color(red)(-1/3))# and #(color(blue)(-2/3), color(orange)4)#

Point-slope form looks like this:

#y - color(red)(y_0) = ((color(orange)(y_1) - color(red)(y_0))/(color(blue)(x_1) - color(limegreen)(x_0)))(x-color(limegreen)(x_0))#

So to write the equation of this line in point-slope form, we need to plug in the points given as follows:

#y - (color(red)(-1/3)) = ((color(orange)4-(color(red)(-1/3)))/(color(blue)(-2/3)-color(limegreen)(3/2)))(x-color(limegreen)(3/2))#

And simplify like this:

#y + 1/3 = ((4+1/3)/(-4/6-9/6))(x-3/2)#

#y + 1/3 = ((13/3)/(-13/6))(x-3/2)#

#y + 1/3 = ((6*cancel13)/(-3*cancel13))(x-3/2)#

#y+1/3 = -2(x-3/2)#

Final Answer