Question

Last year, alayah ordered 4 cubic yards of soil and spent $220. this year, she orders 7 cubic yards of soil and spends $340. write the equation of the linear function that models the relationship between the number of cubic yards of soil ordered and the total cost. enter your answer in y=mx b form.

(a) y=60x+40y=60x+40
(b) y=60x+140y=60x+140
(c) y=40x+60y=40x+60
(d) y=140x+60y=140x+60

Answer 1

The correct equation that shows the linear function of the modeled relationship is y = 40x + 60 which is option c

let x be the cubic yards of soil

and y be the cost for purchasing

general form of linear equation is y = mx + c

if y = 220, then x = 4

220 = 4m + c ------- 1

if y = 340, then x = 7

which means

340 = 7m + c -------------2

subtract equation 1 from 2, you have

120 = 3m

3m = 120

m = 40

substitute m = 40 in equation 1

220 = 4(40) + c

c = 220 - 160

c = 60

Therefore the equation is y = 40x + 60