Question

input (x) output (y) (x,y) -1 -3 (-1,-3) 0 -1 (0,-1) 1 1 (1,1) 2 3 (2,3) what is the shape of the graph? u - shape wave straight line curve

Explanation:

To determine the shape, we can check the relationship between \(x\) and \(y\). Let's find the slope between consecutive points. For \((-1, -3)\) and \((0, -1)\), slope \(m=\frac{-1 - (-3)}{0 - (-1)}=\frac{2}{1} = 2\). For \((0, -1)\) and \((1, 1)\), slope \(m=\frac{1 - (-1)}{1 - 0}=\frac{2}{1}=2\). For \((1, 1)\) and \((2, 3)\), slope \(m=\frac{3 - 1}{2 - 1}=\frac{2}{1}=2\). Since the slope is constant (\(m = 2\)), the graph is a straight line (linear relationship, \(y=2x - 1\) when we check \(y=mx + b\) with \((0,-1)\) giving \(b=-1\)).

Answer:

straight line