nick and his cousin sara have the same birthday but nick is two years younger than sara let the variable x represent nicks age and y represent saras age which graph represents the relationship between nicks age and saras age on a graph
The most appropriate graph to represent the relationship between Nick's age (x) and Sara's age (y) would be a straight line with a positive slope.
Explanation: Since Nick is two years younger than Sara, for any given age (x) of Nick, Sara's age (y) would be x + 2. The relationship can be directly represented as y = x + 2. In this equation, y is the dependent variable representing Sara's age, and x is the independent variable representing Nick's age.
Therefore, on a graph, Nick's age (x) would be plotted on the x-axis, and Sara's age (y) would be plotted on the y-axis. The resulting line would have a positive slope of 1 (which represents that Sara's age increases by 1 year for every 1 year increase in Nick's age) and a y-intercept of 2 (representing that Sara is 2 years older than Nick from the start).
To represent the relationship between Nick's age (x) and Sara's age (y) on a graph, we can use a scatter plot.
On the x-axis, we will plot Nick's age (x), and on the y-axis, we will plot Sara's age (y).
Since Nick is two years younger than Sara, we can represent this relationship by drawing a line that is slanted upwards and moves from left to right. This means that as Nick's age (x) increases, Sara's age (y) also increases. The line will have a positive slope of 1, indicating that for every 1 unit increase in Nick's age, Sara's age also increases by 1.
The graph would look like this:
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0 x-axis (Nick's age)
Here, the line represents the relationship between Nick's age and Sara's age. Each data point on the line will correspond to their same birthday, with Nick's age (x) on the x-axis and Sara's age (y) on the y-axis.
To represent the relationship between Nick's age (x) and Sara's age (y), you can plot their ages on a graph.
Since Nick is two years younger than Sara, we need to consider this difference. We can start by choosing values for Sara's age and then subtracting two from each value to get Nick's age.
Let's assume Sara's age is 10. In that case, Nick's age would be 10 - 2 = 8. So one point on the graph would be (8, 10).
Similarly, if Sara's age is 20, Nick's age would be 20 - 2 = 18. So another point on the graph would be (18, 20).
By plotting several points following this pattern, you will see that the graph will be a straight line that slopes upward from left to right. The line would pass through the points (8, 10) and (18, 20), and continue in that manner.
Thus, the graph representing the relationship between Nick's age and Sara's age would be a straight line with a positive slope.