Question

7. Critique Reasoning The table on the right and the equation y = 8x + 5 describe linear functions. A student states incorrectly that the initial values of the functions are equal. Compare the initial values of the functions. What mistake did the student likely make?

Answer 1

The mistake that the student likely make is thinking about the slope of y = 8x + 5 instead of the initial value, which is 5.

What mistake did the student make?

We want to compare the equatio y = 8x + 5 with the table.

Now, the equation in the table is likely a linear equation which we can write as:

y = a*X + b

where b is the y-intercept. We can see in the table that we have the pair (0, 8), then:

b = 8

The initial value is 8, while the initial value of y = 8x + 5 is 5, clearly, the iniital values are different.

The mistake that the student likely make is thinking about the slope instead of the initial value.

Answer 2

The initial value of a function is the value that it takes when x=0.

From the table, we can see that the value of y that corresponds to x=0 is 8.

Substitute x=0 in the equation to find the initial value:

`\begin{gathered} y=8x+5 \\ =8(0)+5 \\ =0+5 \\ =5 \end{gathered}`

The initial value of the function described by the equation is 5.

Notice that the initial values of those functions are not equal, since the initial value of the function described by the table is 8 and the initial value of the function described by the equation is 5.

Additionally, notice that the coefficient of the linear term on the equation is 8. It is likely that the student thought that it was the initial value.