How do you write the point slope form of the equation given (9,-2) and (-3,2)?

Question

Julia Adams · Accepted Answer

See a solution process below:

First, we need to determine the slope of the equation. 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)(2) - color(blue)(-2))/(color(red)(-3) - color(blue)(9)) = (color(red)(2) + color(blue)(2))/(color(red)(-3) - color(blue)(9)) = 4/-12 = -1/3# 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)(-2)) = color(blue)(-1/3)(x - color(red)(9))# #(y + color(red)(2)) = color(blue)(-1/3)(x - color(red)(9))# We can also substitute the slope we calculated and the values from the second point in the problem giving: #(y - color(red)(2)) = color(blue)(-1/3)(x - color(red)(-3))# #(y - color(red)(2)) = color(blue)(-1/3)(x + color(red)(3))#

Avery Alexander · Answer

undefined To write the point-slope form of the equation given two points (9, -2) and (-3, 2), first find the slope using the formula: m = (y2 - y1) / (x2 - x1). Then, choose one of the points and the slope to write the equation in point-slope form: y - y1 = m(x - x1).