How do you write the point slope form of the equation given (5,-6) and (2,3)?

2 Answers
Apr 30, 2017

See the solution process below:

Explanation:

First, 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)(3) - color(blue)(-6))/(color(red)(2) - color(blue)(5)) = (color(red)(3) + color(blue)(6))/(color(red)(2) - color(blue)(5)) = 9/-3 = -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)(-6)) = color(blue)(-3)(x - color(red)(5))#

Solution 1) #(y + color(red)(6)) = color(blue)(-3)(x - color(red)(5))#

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

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

Apr 30, 2017

#y=-3x+9#

Explanation:

First, find the slope between the points. You can find slope using:

#m=(y_2-y_1)/(x_2-x_1)#

Plug into the formula:

#m=(3-(-6))/(2-5)=9/-3=-3#

Now we have the slope. We can now plug into the point-slope form which is:

#y-y_1=m(x-x_1)#

It doesn't really matter which point we plug in so I'll plug in #(2,3)# since I don't like dealing with negative numbers:

#y-3=-3(x-2)#

Distribute the #-3#:

#y-3=-3x+6#

Add #3# to both sides:

#y=-3x+9#