Question

I need some help with a few word problems.
-A cannery processed 1,445 pounds of strawberries in 4.5 hours. The cannery processed 2,320 pounds in 7 hours. Write a linear equation to model the relationship between the weight of the strawberries S and time T. How many pounds of strawberries can be processed in 11 hours?

Thank you in advance for your help!

Answer 1

Hint. (4.5, 1445) and (7, 2320) are points. Find the slope. Then find the y-intercept , b. Then use y = mx + b to write the equation of the line.

Answer 2

so m=875/2.5? in y=mx+b y=875/2.5x+11?

Answer 3

Show the steps you used to get that please.

Answer 4

\[m=\frac{ 2320-1445 }{ 7-4.5 }\]

\[m=\frac{ 875 }{ 2.5}\]

\[y=\frac{ 875 }{ 2.5 }x+11\]
11 being the number of hours. right?

Answer 5

Are those the correct steps?

Answer 6

You didn't solve for b properly.

\(x\) represents hours
\(y\) represents pounds of strawberries.

To solve for b, you need to input the slope and a point in to the formula:

y = mx + b

Assuming your slope is correct, you input one of the points \((x,y) = \color\green{(4.5, 1445)}\) and the slope \(m = \color\red{(875/2.5)}\)

\(\color\green{1445} = \color\red{(875/2.5)}\color\green{(4.5)} + b\)

Answer 7

Then solve for \(b\). Once you have solved for \(b\). Then you can re-write your equation of the line but only include the values of \(m\) and \(b\)