Which line has the greatest rate of change? A. The line passing through (0, 2) and (4, 10)
B. The line passing through (0,5) and (2,8)
C. The line passing through (0,0) and (3,-4)
D. The line passing through (0,6) and (12,9)

Greetings from Brasil

The rate of change between 2 points is obtained through the expression:

a) (0, 2) and (4, 10) so, X₁ = 0; X₂ = 4; Y₁ = 2 and Y₂ = 10

m = ΔY/ΔX

m = (Y₂ - Y₁)/(X₂ - X₁)

m = (10 - 2)/(4 - 0)

m = 8/4 = 2

b) (0,5) and (2,8) so, X₁ = 0; X₂ = 2; Y₁ = 5 and Y₂ = 8

m = ΔY/ΔX

m = (Y₂ - Y₁)/(X₂ - X₁)

m = (8 - 5)/(2 - 0)

m = 3/2

c) (0,0) and (3,-4) so, X₁ = 0; X₂ = 3; Y₁ = 0 and Y₂ = - 4

m = ΔY/ΔX

m = (Y₂ - Y₁)/(X₂ - X₁)

m = (- 4 - 0)/(3 - 0)

m = -4/3

d) (0,6) and (12,9) so, X₁ = 0; X₂ = 12; Y₁ = 6 and Y₂ = 9

m = ΔY/ΔX

m = (Y₂ - Y₁)/(X₂ - X₁)

m = (9 - 6)/(12 - 0)

m = 3/12 ⇔ m = 1/4

Among all the values above, the largest is 2, so points

(0; 2) and (4; 10)

282 6/7 cm^2

step-by-step explanation:

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent