The line joining (3, p) to (7, –4p) is parallel to the line joining (–1, –3) to (3, 7). Find p.

p = - 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m =

with (x₁, y₁ ) = (- 1, - 3) and (x₂, y₂ ) = (3, 7)

m = = = =

Parallel lines have equal slopes

Calculate the slope of the other 2 points and equate to

with (x₁, y₁ ) = (3, p) and (x₂, y₂ ) = (7, - 4p)

m = = = ( cross- multiply )

- 10p = 20 ( divide both sides by - 10 )

p = - 2