Question

A cannery canbprocess 1445 pounds of strawberries in 4.5 hours the cannery process 2320 pounds in seven hours write a linear equation to model the relationship between the weight of strawberries S and the time t how many pounds of strawberries be processed in 11 hours

Answer 1

(4.5, 1445)(7, 2320)
slope = (2320 - 1445) / (7 - 4.5) = 875/2.5 = 350

y = mx + b
slope(m) = 350
(7,2320)...x = 7 and y = 2320
now we sub and find b, the y int
2320 = 350(7) + b
2320 = 2450 + b
2320 - 2450 = b
-130 = b

so ur equation is gonna be : y = 350x - 130...or s = 350t - 130

s = 350t - 130.....when t = 11
s = 350(11) - 130
s = 3850 - 130
s = 3720.....so 3720 lbs can be processed in 11 hrs

Answer 2

We have two points:(4.5 , 1445) and (7 , 2320);
Given two points (x₁,y₁) and (x₂,y₂), the equation of the line (point-slope form) would be:
m=the slope.
m=(y₂-y₁)/(x₂-x₁)

y-y₁=m(x-x₁)              or              y-y₂=m(x-x₂)

In this case:
1) we calculate the slope:
m=(y₂-y₁)/(x₂-x₁)
m=(2320-1445)/(7-4.5)
m=350

2) In this case, we rename, and:
y=S
x=t

3) we build the equation:
S-S₁=m(t-t₀)
m=350
(4.5 , 1445)

S-1445=350(t-4.5)
S=350t-1575+1445
S=350t-130

if t=11
S=350t-130
S=350(11)-130
S=3850-130
S=3720

Answer: the equation would be:  S=350t-130, and the amount of pounds of strawberries processed in 11 hours is 3720.