Question

PLZ HELP ASAP!!!!!!!! DUE TOMORROW!!

the graph shows numbers of servings in different amounts of frozen yogurt listed on a carton. write an equation that gives the number of servings y in x pints. explain how to do it.

Answer 1

`y=2.5x`

Explanation:

We have been given a graph that shows numbers of servings (y) in different amounts (x) of frozen yogurt listed on a carton.

To write an equation that gives the number of servings y in x pints, we will have to find the slope (rate of change) of our given linear function.

Since we know that rate of change of a function can be found by vertical change of the function divided by horizontal change of the function.

`m=(y_2-y_1)/(x_2-x_1)`

m= Slope (rate of change).

`y_2-y_1`=Difference between two y-coordinates.

`x_2-x_1`=Difference between corresponding x-coordinates of the y-coordinates.

Upon substituting coordinates of two points (0,0) and (4,10) in slope formula we will get,

`m=(10-0)/(4-0)`

`m=(10)/(4)`

`m=2.5`

The slope of our given line is 2.5.

Now we will write equation of our given line is slope-intercept form. The equation of a line in slope-intercept form is:
`y=mx+b`, where m=slope and b = y-intercept (initial value).

Upon substituting m=2.5 and coordinates of point (4,10) in slope-intercept form of equation we will get,

`10=2.5* 4+b`

`10=10+b`

`10-10=b`

`0=b`

Upon substituting m=2.5 and b=0 in slope-intercept form of equation we will get,

`y=2.5x+0`

`y=2.5x`

Therefore, the equation
`y=2.5x` will give the number of servings y in x pints.