Question

each graph below shows a relationship between x and y.
for each graph, determine whether x and y are proportional.
if x and y are proportional, fill in the blank with a number.
graph 1
graph of a line with points at (0,2), (1,5), (2,8)
○ proportional
y is □ times x
○ not proportional
graph 2
graph of a line with points at (0,0), (1,6), (2,12)
○ proportional
y is □ times x
○ not proportional

Explanation:

Step1: Analyze Graph 1

A proportional relationship has a graph that passes through the origin \((0,0)\) and is a straight line. Graph 1 has a \(y\)-intercept at \((0,2)\), not \((0,0)\). So, it's not proportional.

Step2: Analyze Graph 2

Graph 2 passes through the origin \((0,0)\) and is a straight line. Let's find the constant of proportionality \(k\) (where \(y = kx\)). When \(x = 1\), \(y = 6\) (from the point \((1,6)\)). So \(k=\frac{y}{x}=\frac{6}{1}=6\). So \(y\) is 6 times \(x\), and it's proportional.

Answer:

Graph 1: Not proportional
Graph 2: Proportional, \(y\) is \(6\) times \(x\)