Question

Find the values of k and b if it is known that the graph of y=kx+b goes through points (2, 10) and (−7, −10).Plz help i dont get it

Answer 1

k =
`(20)/(9)` and b =
`(50)/(9)`

Given 2 points that lie on the graph of y = kx + b then the coordinates of these points will make the equation true. Substituting the coordinates into the equation allows us to find k and b

(2, 10) → 10 = 2k + b → (1)

( - 7, - 10) → - 10 = - 7k + b → (2)

subtracting (2) from (1) term by term gives

(10 - (- 10)) = (2k - (- 7k)) + (b - b)

20 = 9k → ( divide both sides by 9)

k =
`(20)/(9)`

Substitute this value into ( 1) or (2) and solve for b

(1) → 10 = (2 ×
`(20)/(9)`) + b

hence b =
`(90)/(9)` -
`(40)/(9)` =
`(50)/(9)`