How do you write the equation in point slope form given (5,7) and (-1,3)?

Question

Ethan Adkins · Accepted Answer

#(y - color(red)(7)) = color(blue)(2/3)(x - color(red)(5))#

Or

#(y - color(red)(3)) = color(blue)(2/3)(x + color(red)(1))# First, we must determine 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 points in the problem gives: #m = (color(red)(3) - color(blue)(7))/(color(red)(-1) - color(blue)(5))# #m = (-4)/-6 = 2/3# 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. We can substitute the slope we calculate and the first point to give: #(y - color(red)(7)) = color(blue)(2/3)(x - color(red)(5))# Or, we can substitute the slope we calculate and the second point to give: #(y - color(red)(3)) = color(blue)(2/3)(x - color(red)(-1))# #(y - color(red)(3)) = color(blue)(2/3)(x + color(red)(1))#

Kennedy Adams · Answer

undefined To write the equation in point-slope form given the points (5,7) and (-1,3), use the formula: y - y₁ = m(x - x₁), where (x₁, y₁) is one of the given points, and m is the slope calculated using the two points. Then, plug in the values of the slope and one of the points into the formula.