Question

Which proportion can be used to show that the slope of JL is equal to the slope of MP? (sorry for the horrible quality)

Answer 1

The proportion can be used to show that the slope of JL is equal to the slope of MP is
`(0-4)/(-4-(-7))` =
`(-4-8)/(-1-(-10))` ⇒ G

Explanation:

The rule of the slope of a line is
`m=(y2-y1)/(x2-x1)` , where (x1, y1) and (x2, y2) are two points on the line

∵ The coordinates of the point J are (-7, 4)

∵ The coordinates of the point L are (-4, 0)

∴ x1 = -7 and y1 = 4

∴ x2 = -4 and y2 = 0

→ Substitute them in the rule above to find the slope of LJ

∴
`m_(JL)=(0-4)/(-4-(-7))`

∵ The coordinates of the point M are (-10, 8)

∵ The coordinates of the point P are (-1, -4)

∴ x1 = -10 and y1 = 8

∴ x2 = -1 and y2 = -4

→ Substitute them in the rule above to find the slope of MP

∴
`m_(MP)=(-4-8)/(-1-(-10))`

∵ The slope of JL = the slope of MP

∴
`(0-4)/(-4-(-7))` =
`(-4-8)/(-1-(-10))`

The proportion can be used to show that the slope of JL is equal to the slope of MP is
`(0-4)/(-4-(-7))` =
`(-4-8)/(-1-(-10))`