Question

The points (-6,r) and (2,5) lie on a line with slope -1/4. Find the missing coordinate r.

Answer 1

r = 7

Explanation:

Calculate the slope using the slope formula then equate to -
`(1)/(4)`

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

with (x₁, y₁ ) = (- 6, r ) and (x₂, y₂ ) = (2, 5 )

m =
`(5-r)/(2-(-6))` =
`(5-r)/(2+6)` =
`(5-r)/(8)` , then

`(5-r)/(8)` = -
`(1)/(4)` ( multiply both sides by 8 to clear the fractions )

5 - r = - 2 ( subtract 5 from both sides )

- r = - 7 ( multiply both sides by - 1 )

r = 7

Answer 2

`\displaystyle 7`

Step-by-step explanation:

`\displaystyle (-y_1 + y_2)/(-x_1 + x_2) = m\\ \\ (-r + 5)/(6 + 2) = m \Rightarrow (-r + 5)/(8) \hookrightarrow -(2)/(8) = -(1)/(4) \\ \\ \boxed{7 = r}`

I am joyous to assist you at any time.