Question

A line passes through the point (-2,7) and. Has a slope of -4. What is the value of a if the point (a, -2) is also on the line?

Answer 1

a =
`(1)/(4)`

using the ' gradient formula ' m = (y₂ - y₁)/(x₂ - x₁) → (m is the slope)

here (x₁, y₁) = (a , - 2)) and (x₂ , y₂) = (- 2, 7)

thus
`((7 + 2))/((-2 - a))` = -4 ⇒
`(9)/((- 2 - a))` = -4

cross-multiply

-4(- 2 - a) = 9

8 + 4a = 9

subtract 8 from both sides

4a = 9 - 8 =
`(1)/(4)`1

divide both sides by 4

a =
`(1)/(4)`