Question

the graph shows the relationship between time and number of soda bottle a machine can make. Use the points (4,160) and (7280) to find the number of soda bottles the machine can make each minute.

Answer 1

40 soda each minute

Explanation:

we are given two points (4,160),(7,280)

we want to figure out" the number of soda bottles the machine can make each minute."

remember that, to figure out how many soda bottles the machine can make each time is the same thing as to figure out the slope (average rate of change) of the given points

recall that,

`\displaystyle m = ( y_(2) - y _(1) )/(x _(2) - x _(1))`

let's the starting and ending points be (4,160) and (7,280) respectively thus,

`y_2=280\\y_1=160\\x_2=7\\x_1=4`

substitute

`\displaystyle m = ( 280- 160 )/(7 - 4)`

simplify substitution:

`\displaystyle m = ( 120 )/(3)`

simplify division:

`\displaystyle m = 40`

therefore,

the machine can make 40 soda each minute

Answer 2

• 40 bottles

Explanation:

This represents a proportional relationship.

The equation for proportional relationship is:

• y = kx

In the given case we have:

• y- number of soda bottles made in x minutes, k- the number of bottles made in one minute

Use either point to work out the value of k:

• 160 = k*4
• k = 160/4
• k = 40