Question

1. consider the table below: x y 2 10 5 6 8 2 11 -2 what is the change of y? (how is y changing?) △y = what is the change of x? (how is x changing?) △x = what is the rate of change? (also known as slope) $\frac{\triangle y}{\triangle x}=$ leave the answer as a fraction

Explanation:

Step1: Calculate change in Y

Take two - consecutive y - values. Let's take the first two points \((2,10)\) and \((5,6)\). \(\Delta Y=y_2 - y_1\). Using the first two points, \(y_1 = 10\) and \(y_2=6\), so \(\Delta Y=6 - 10=- 4\). We can check with other consecutive points. For example, taking \((5,6)\) and \((8,2)\), \(\Delta Y=2 - 6=-4\). So \(\Delta Y=-4\).

Step2: Calculate change in X

Take two - consecutive x - values. Using the first two points \((2,10)\) and \((5,6)\), \(\Delta X=x_2 - x_1\), where \(x_1 = 2\) and \(x_2 = 5\), so \(\Delta X=5 - 2 = 3\). Checking with other consecutive points, for example, taking \((5,6)\) and \((8,2)\), \(\Delta X=8 - 5=3\). So \(\Delta X = 3\).

Step3: Calculate rate of change (slope)

The rate of change (slope) \(m=\frac{\Delta Y}{\Delta X}\). Since \(\Delta Y=-4\) and \(\Delta X = 3\), then \(m=\frac{-4}{3}\).

Answer:

\(\Delta Y=-4\)
\(\Delta X = 3\)
\(\frac{\Delta Y}{\Delta X}=-\frac{4}{3}\)