How do you write the point slope form of the equation given (3,-3) and (5,0)?

Question

Ethan Adkins · Accepted Answer

See a solution process below:

First, we need to determine the slope of the line represented by the two points in the problem. 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)(0) - color(blue)(-3))/(color(red)(5) - color(blue)(3)) = (color(red)(0) + color(blue)(3))/(color(red)(5) - color(blue)(3)) = 3/2# 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. Substituting the slope we calculated and the values from the first point gives: #(y - color(red)(-3)) = color(blue)(3/2)(x - color(red)(3))# #(y + color(red)(3)) = color(blue)(3/2)(x - color(red)(3))# We can also substitute the slope we calculated and the values from the second point giving: #(y - color(red)(0)) = color(blue)(3/2)(x - color(red)(5))# Or #y = color(blue)(3/2)(x - color(red)(5))#

Avery Alexander · Answer

undefined The point-slope form of the equation given the points (3, -3) and (5, 0) is $ y - y_1 = m(x - x_1) $, where $ (x_1, y_1) $ is a point on the line, and $ m $ is the slope. First, calculate the slope using the formula $ m = \frac{y_2 - y_1}{x_2 - x_1} $ with the given points. Then, substitute the slope and one of the points into the point-slope form to get the equation. The slope is $ m = \frac{0 - (-3)}{5 - 3} = \frac{3}{2} $. Substituting $ (3, -3) $ as $ (x_1, y_1) $ into the point-slope form, the equation is $ y - (-3) = \frac{3}{2}(x - 3) $. Simplify to get $ y + 3 = \frac{3}{2}(x - 3) $.