If g= (1,1),(2,3),(3,5),(4,7) is a function described by the formula, g ( x )=α x +β then what values should be assigned to α and β ?

Question

If g= (1,1),(2,3),(3,5),(4,7) is a function described by the formula, g ( x )=α x +β then what values should be assigned to α and β ? (A) α=1, β=1 (B) α=2, β=-1 (C) α=1, β=-2 (D) α=-2, β=-1

Tardigrade Admin · Accepted Answer

(1,1) satisfies g(x)=α x+β ∴ α+β=1 (2,3) satisfies g(x)=α x+β ∴ 2 α+β=3 Solving the two equation, we get α=2, β=-1 It can be checked that other ordered pairs satisfy g(x)=2 x-1

Q. If $g = {(1, 1), (2, 3), (3, 5), (4, 7)}$ is a function described by the formula, $g (x) = αx + β$ then what values should be assigned to $α$ and $β ?$

$α = 1, β = 1$

$α = 2, β = - 1$

$α = 1, β = - 2$

$α = - 2, β = - 1$

$(1, 1)$ satisfies $g (x) = αx + β$
$∴ α + β = 1$
$(2, 3)$ satisfies $g (x) = αx + β$
$∴ 2 α + β = 3$
Solving the two equation, we get
$α = 2, β = - 1$
It can be checked that other ordered pairs satisfy
$g (x) = 2 x - 1$

Q. If g={(1,1),(2,3),(3,5),(4,7)} is a function described by the formula, g(x)=αx+β then what values should be assigned to α and β?

α=1,β=1

α=2,β=−1

α=1,β=−2

α=−2,β=−1