Question

Find the value of k so that the line passing through the given points has slope m. Write an equation of the line in point-slope form.

(k, 4k), (k+2,3k), m = -1

Answer 1

You can find the value of k by using the slope formula, m =
`(y_(2) - y_(1))/(x_(2) - x_(1))`, where m is the slope and
`x_(1)`,
`y_(1)`,
`x_(2)`, and
`y_(2)` are coordinate pairs on the line.

m =
`(y_(2) - y_(1))/(x_(2) - x_(1))` Plug in the values
-1 =
`(3k - 4k)/(k + 2 - k)` Subtract 3k and 4k
-1 =
`(-k)/(k + 2 - k)` Subtract k and k
-1 =
`(-k)/(2)` Multiply both sides by 2
-2 = -k Divide both sides by -1
2 = k

Now, replace two with k in the coordinates to figure out the actual numbers.
(k, 4k) and (k + 2, 3k) Plug in 2
(2, 4(2)) and (2 + 2, 3(2)) Simplify
(2, 8) and (4, 6)

Now, choose one of those coordinates and plug it into the point-slope equation (
`y - y_(1) = m (x - x_(1))`). I'll use (2, 8).


`y - y_(1) = m (x - x_(1))` Plug in slope and the coordinate
y - 8 = -1 (x - 2)