Question

If the line containing the points (x,5) and (7,14) is parallel to another line with slope -3, find x. Explain

Answer 1

x = 10

Explanation:

Parallel lines have equal slopes.

calculate the slope of the line containing the 2 points and equate to - 3

using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (x, 5 ) and (x₂, y₂ ) = (7, 14 )

m =
`(14-5)/(7-x)` =
`(9)/(7-x)`

Equating m to - 3

`(9)/(7-x)` = - 3 ← multiply both sides by 7 - x to clear the fraction

9 = - 3(7 - x) ( divide both sides by - 3 )

- 3 = 7 - x ( subtract 7 from both sides )

- 10 = - x ( multiply both sides by - 1 ) , then

x = 10