Describe and correct the error a student made when finding the function rule for the data in the table. Select the correct choice below and fill in the answer box(es) to complete your choice. A. The student read the table incorrectly. When x1, y 10. The correct function rule is y 9 x plus 10. B. When x increases by 1, y increases by nothing rather than by 9. The correct function rule is y nothing. C. The student should have used x0 to find the constant term, not x1. When x0, y nothing. The correct function rule is y nothing.

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MrRoyal MrRoyal · Answer 1 · 2021-10-06T14:23:44+02:00

The question is an illustration of a linear equation or function.

The true statement is: B. When x increases by 1, y increases by 9. The correct function rule is [tex]\mathbf{y = 9x + 1}[/tex]

From the table, we have the following observations:

This means that, the slope of the table is 9

A linear function is represented as:

[tex]\mathbf{y = mx + b}[/tex]

Where:

[tex]\mathbf{m \to slope}[/tex]

[tex]\mathbf{b \to y-intercept}[/tex] --- the value of y, when x = 0

So, we have:

[tex]\mathbf{m = 9}[/tex]

[tex]\mathbf{y = mx + b}[/tex] becomes

[tex]\mathbf{y = 9x + b}[/tex]

Recall that:

An increment of 1 in the value of x would result in an increment of 9 in the value of y

This means that:

If x is reduced by 1, the corresponding value of y would reduce by 9

When

[tex]\mathbf{x = 1, y = 10}[/tex]

Reduce x by 1 (this means y would reduce by 9)

So, we have:

[tex]\mathbf{x = 0, y = 1}[/tex]

Recall that:

[tex]\mathbf{b \to y-intercept}[/tex] --- the value of y, when x = 0

This means that:

[tex]\mathbf{b = 1}[/tex]

Substitute [tex]\mathbf{b = 1}[/tex] in [tex]\mathbf{y = 9x + b}[/tex]

[tex]\mathbf{y = 9x + 1}[/tex]

Hence, the complete statement is:

B. When x increases by 1, y increases by 9. The correct function rule is [tex]\mathbf{y = 9x + 1}[/tex]