Question

the table represents a linear function. the rate of change between the points \\((-5, 10)\\) and \\((-4, 5)\\) is \\(-5\\). what is the rate of change between the points \\((-3, 0)\\) and \\((-2, -5)\\)?

\\(\

$$\begin{array}{|c|c|}\\hline x & y \\\\\\hline -5 & 10 \\\\\\hline -4 & 5 \\\\\\hline -3 & 0 \\\\\\hline -2 & -5 \\\\\\hline\\end{array}$$

\\)

• \\(-5\\)
• \\(-\frac{1}{5}\\)
• \\(\frac{1}{5}\\)
• \\(5\\)

Explanation:

Identify the given points

$$ (x_1, y_1) = (-3, 0),\quad (x_2, y_2) = (-2, -5) $$

Apply the rate of change formula

$$ \text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 0}{-2 - (-3)} $$

Simplify the expression

$$ \frac{-5}{-2 + 3} = \frac{-5}{1} = -5 $$

Answer:

• (A) \(-5\) (Correct answer)
• (B) \(-\frac{1}{5}\)
• (C) \(\frac{1}{5}\)
• (D) \(5\)