each graph below shows a relationship between x and y. for each graph, determine whether x and y are…
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 2 proportional y is times x proportional y is times x not proportional not proportional
Answer
Explanation:
Step1: Recall proportional - relationship criteria
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 $(0,0)$. So, $x$ and $y$ are not proportional.
Step3: Analyze Graph 2
The line in Graph 2 passes through the origin $(0,0)$. To find the constant of proportionality $k$, we can use the formula $y = kx$. Let's take a point on the line, say $(2,5)$. Then $k=\frac{y}{x}=\frac{5}{2}=2.5$.
Answer:
Graph 1: Not proportional Graph 2: Proportional, $y$ is $2.5$ times $x$