Question

Х101112y27a11In order for the data in the table to represent a linearfunction with a rate of change of -8, what must be thevalue of a?a = 2O a = 3a = 19O a = 35

Answer 1

a = 19

Step-by-step explanation

First, note that the rate of change of a linear function is known as its slope.

Given the coordinates (x1, y1) and (x2, y2), the formula for calculating the slope is expressed as;

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

Using the coordinates (10, 27) and (11, a) where m = -8, substitute the values into the formula;

`\begin{gathered} (a-27)/(11-10)=-8 \\ (a-27)/(1)=-8 \\ a-27=-8 \end{gathered}`

Add 27 to both sides as shown;

`\begin{gathered} a-27+27=-8+27 \\ a=27-8 \\ a=19 \end{gathered}`

Hence the value of a is 19