How do you write an equation in point slope form given (p,q), (-p, 2q)?

Question

Ethan Adkins · Accepted Answer

#(y - color(red)(q)) = color(blue)(-q/(2p))(x - color(red)(p))#

or

#(y - color(red)(2q)) = color(blue)(-q/(2p))(x + color(red)(p))# First, we need to determine the slope from the two points given 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 problem gives: #m = (color(red)(2q) - color(blue)(q))/(color(red)(-p) - color(blue)(p))# #m = q/-2p = -q/(2p)# Now we can use either point to build a equation in the point-slope form: 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. Solution for point (p, q): #(y - color(red)(q)) = color(blue)(-q/(2p))(x - color(red)(p))# Solution for point (-p, 2q): #(y - color(red)(2q)) = color(blue)(-q/(2p))(x - color(red)(-p))# #(y - color(red)(2q)) = color(blue)(-q/(2p))(x + color(red)(p))#

Julia Adams · Answer

undefined To write an equation in point-slope form given two points (p, q) and (-p, 2q), you first need to find the slope (m) using the formula:

m = (change in y) / (change in x)

Once you have the slope, you can choose either of the two points to plug into the point-slope form equation:

y - y₁ = m(x - x₁)

Substitute the slope and the coordinates of the chosen point into the equation, and simplify if necessary to obtain the final equation in point-slope form.