Question

which graph matches this table? input (x) -1 0 1 output (y) 5 3 1

Explanation:

Step1: Identify the points from the table

The table gives us the points \((-1, 5)\), \((0, 3)\), and \((1, 1)\).

Step2: Analyze the slope

First, calculate the slope \(m\) between two points. Let's take \((-1, 5)\) and \((0, 3)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). So, \(m=\frac{3 - 5}{0 - (-1)}=\frac{-2}{1}=-2\).

Step3: Analyze the y - intercept

When \(x = 0\), \(y = 3\), so the y - intercept \(b = 3\). The equation of the line is \(y=-2x + 3\).

Step4: Check the graphs

• For the first graph: The line has a positive slope, which does not match our slope of \(-2\), so we can eliminate it.
• For the second graph: Let's check the points. When \(x=-1\), \(y=-2\times(-1)+3 = 2 + 3=5\); when \(x = 0\), \(y = 3\); when \(x = 1\), \(y=-2\times1+3 = 1\). These points match the table.
• For the third graph: When \(x = 0\), the y - value is \(2\) (from the graph), but our y - intercept is \(3\), so we can eliminate it.

Answer:

The second graph (the middle one)