Question

a grocery bag containing 4 potatoes weighs 2 pounds. An identical bag contains 12 potatoes weighs 4 pounds. Write an equation in standard form that shows the relationship of the weight (y) and the number of potatoes (x).

Answer 1

Answer with Step-by-step explanation:

Let, the equation which represents  relationship of the weight (y) and the number of potatoes (x) be

y=mx+c

y=2 when x=4

i.e. 4m+c=2 -------(1)

and y=4 when x=12

i.e. 12m+c=4   --------(2)

Subtracting equation (1) from (2), we get

8m=2

i.e. m=1/4

Putting value of m in (1), we get

1+c=2

i.e. c=1

So,  an equation in standard form that shows the relationship of the weight (y) and the number of potatoes (x) is:

y= $\dfrac{1}{4}x+1$

Answer 2

Use the ordered pairs to first find the slope then substitution into y=mx+b to find b