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 = $\frac{20}{9}$ and b = $\frac{50}{9}$

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 = $\frac{20}{9}$

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

(1) → 10 = (2 × $\frac{20}{9}$) + b

hence b = $\frac{90}{9}$ - $\frac{40}{9}$ = $\frac{50}{9}$