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 proportional y is times x not proportional graph 2 proportional y is times x not proportional

Explanation:

Step1: Recall proportional - relationship condition

Two variables \(x\) and \(y\) are proportional if the graph is a straight - line passing through the origin \((0,0)\).

Step2: Analyze Graph 1

The line in Graph 1 does not pass through the origin \((0,0)\) (it intersects the \(y\) - axis at \(y = 4\)). So, \(x\) and \(y\) are not proportional.

Step3: Analyze Graph 2

The line in Graph 2 passes through the origin \((0,0)\). Let's find the constant of proportionality \(k\) using the formula \(y=kx\). We can take a point on the line, say \((1, 5)\). Substitute \(x = 1\) and \(y = 5\) into \(y=kx\), we get \(5=k\times1\), so \(k = 5\).

Answer:

Graph 1: Not proportional
Graph 2: Proportional, \(y\) is \(5\) times \(x\)