First, we must find 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 two points in the problem gives:
#m = (color(red)(-6) - color(blue)(3))/(color(red)(4) - color(blue)(2))#
#m = -9/2#
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.
Now we can use the slope we calculated and the first point to give:
#(y - color(red)(3)) = color(blue)(-9/2)(x - color(red)(2))#
We can also use the slope we calculated and the second point to give:
#(y - color(red)(-6)) = color(blue)(-9/2)(x - color(red)(4))#
#(y + color(red)(6)) = color(blue)(-9/2)(x - color(red)(4))#
