Question

The graph depicts the growth and costs using of line segment use the midpoint formula to approximate the cost during the year 1987

Answer 1

Answer:

The approximate cost during the year 1987 was $7,533

Step-by-step explanation:

The complete question in the attached figure

we have

y -----> is the cost in dollars

x -----> is the year

Looking at the graph we have the points

(1983,5,047) and (1991, 10,019)

To determine the cost in the year 1987, find out the midpoint between the two given points

The formula to calculate the midpoint between two points is equal to

$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

substitute the values

$M=(\frac{1983+1991}{2},\frac{5,047+10,019}{2})$

$M=(1987,7,533)$

therefore

The approximate cost during the year 1987 was $7,533

Answer 2

The cost during the year 1987 in the graph that depicts the growth and costs is 7509.5.

What is the equation of the graph?

We know that the function is a simple line therefore we will use the general equation to depict the line given,

y =mx +c

What is the slope of the graph?

We know that the slope of the graph can be found using the points given,

Point 1 = (1983, 5000)

Point 2 = (1991, 10019)

$m = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{10019-5000}{1991-1983} = 627.375$

What is the value of the constant?

We know the two points on the graph, therefore  the value of the constant c can be found by substituting the value of the points in the graph,

$5000 =(627.375)1983 +c\\\\c= -1239084.625$

Thus, the value of the constant is -1239084.625.

What is the approximate cost during the year 1987?

We already know the equation of line substitute the values,

$y = mx+c\\y = 627.375(1987)-1239084.625\\\\y = 7,509.5$

Hence, the cost during the year 1987 in the graph that depicts the growth and costs is 7509.5.

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