Question

The pair of points (5, 6) and (10, y) lie on a line with a slope of 4/5. Set up and solve for the missing y-value using the slope formula. Show all work.

Answer 1

y = 10

Explanation:

calculate the slope m of the 2 points using the slope formula and equate to the given slope.

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

with (x₁, y₁ ) = (5, 6 ) and (x₂, y₂ ) = (10, y )

m =
`(y-6)/(10-5)` =
`(y-6)/(5)`

equate this expression for m to the given m of
`(4)/(5)`

`(y-6)/(5)` =
`(4)/(5)` ( cross- multiply )

5(y - 6) = 20 ( divide both sides by 5 )

y - 6 = 4 ( add 6 to both sides )

y = 10