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The table shows the cost y (in dollars) of x pounds of sunflower seeds.


a. What is the missing y-value that makes the table represent a linear function?

The missing y-value is

b. Write a linear function that represents the cost y of x pounds of seeds. Interpret the slope.

c. Does the function have a maximum value? Explain your reasoning.
The function _ have a maximum value because you _ increase the cost by increasing the amount of sunflower seeds purchased.

The table shows the cost y in dollars of x pounds of sunflower seeds a What is the missing yvalue that makes the table represent a linear function The missing y class=

Respuesta :

Part a: The missing y - value is [tex]4.20[/tex]

Part b: The linear function is [tex]y=1.4x[/tex] and slope is [tex]1.4[/tex]

Part c: The function does not have a maximum value.

Explanation:

Part a: From the table we can see that the change in x, is a constant.

To determine the missing y -  value, we have,

[tex]\frac{y}{3} =\frac{2.80}{2}[/tex]

Simplifying, we get,

[tex]\frac{y}{3} =1.40[/tex]

[tex]y=4.20[/tex]

Thus, the missing y - value is [tex]4.20[/tex]

Part b: The linear function can be determined using the formula,

[tex]y=mx+b[/tex]

First, we shall find the slope using the coordinates [tex](2,2.8)[/tex] and [tex](3,4.20)[/tex]

Slope [tex]m=\frac{4.20-2.80}{1} =1.4[/tex]

The y - intercept can be determined when the value of x is zero. Since, from the table we can see that none of the x-values are zero. Hence, the y - intercept is zero.

Thus, we have, [tex]b=0[/tex]

Substituting [tex]m=1.4[/tex] and [tex]b=0[/tex] in the formula [tex]y=mx+b[/tex], we get,

[tex]y=1.4x[/tex]

Hence, the linear function is given by [tex]y=1.4x[/tex]

Part c:

From the table, we can see that, as the value of x increases, the value of y also increases.

Hence, the function does not have a maximum value.

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