Question

A line contains the points R (-5, -3) S (-1, -1) and T (x, 3). Solve for x. Be sure to show and explain all work.

Answer 1

x = 7

Explanation:

since the points all lie on the same line then the slopes of adjacent points will have the same slope.

calculate the slope using R and S then equate to slope using R and T or S and T

calculate slope using slope formula

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

with (x₁, y₁ ) = R (- 5, - 3 ) and (x₂, y₂ ) = S (- 1, - 1 )

`m_(RS)` =
`(-1-(-3))/(-1-(-5))` =
`(-1+3)/(-1+5)` =
`(2)/(4)` =
`(1)/(2)`

Repeat with (x₁, y₁ ) = R (- 5, - 3 ) and (x₂, y₂ ) = T (x, 3 )

`m_(RT)` =
`(3-(-3))/(x-(-5))` =
`(3+3)/(x+5)` =
`(6)/(x+5 )`

equating
`m_(RS)` and
`m_(RT)`

`(6)/(x+5)` =
`(1)/(2)` ( cross- multiply )

x + 5 = 12 ( subtract 5 from both sides )

x = 7