To determine the appropriate value of \(a\) for the data in the table to represent a linear function with a rate of change (slope) of \(-8\), we need to use the definition of slope for a linear function. The slope \(m\) between any two points \((x_1, y_1)\) and \((x_2, y_2)\) on a straight line is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Given that the rate of change (slope) is \(-8\), we can set up the equation with this information. We need to plug in pairs of \((x, y)\) values and solve for \(a\).
Let’s assume we have the following table:
| \(x\) | \(y\) |
|------|-------|
| 1 | 10 |
| 2 | a |
Now, using the slope formula between the points \((1, 10)\) and \((2, a)\):
\[ -8 = \frac{a - 10}{2 - 1} \]
Simplifying this equation:
\[ -8 = a - 10 \]
Adding 10 to both sides to solve for \(a\):
\[ -8 + 10 = a \]
\[ 2 = a \]
So, in order for the data to represent a linear function with a rate of change of \(-8\), the value of \(a\) must be \(2\).
Therefore, the correct answer is:
\[ a = 2 \]
In order for the data in the table to represent a linear function with a rate of change of –8, what must be the value of a?
a = 2
a = 3
a = 19
a = 35
1 answer