Nick and his cousin Sara have the same birthday, but Nick is four years older than Sara. Let the variable x represent Nick’s age and y represent Sara’s age. Which graph represents the relationship between Nick’s age and Sara’s age?
(1 point)
Responses
The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages.The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 0 comma 4 right parenthesis, left parenthesis 2 comma 6 right parenthesis, and left parenthesis 4 comma 8 right parenthesis.
Image with alt text: The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 0 comma 4 right parenthesis, left parenthesis 2 comma 6 right parenthesis, and left parenthesis 4 comma 8 right parenthesis.
The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages.The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 0 comma 0 right parenthesis, left parenthesis 4 comma one-half right parenthesis, and left parenthesis 8 comma 1 right parenthesis.
Image with alt text: The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 0 comma 0 right parenthesis, left parenthesis 4 comma one-half right parenthesis, and left parenthesis 8 comma 1 right parenthesis.
The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages.The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left-parenthesis 0 comma 0 right-parenthesis, left-parenthesis one-half comma 4 right-parenthesis, and left-parenthesis 1 comma 8 right-parenthesis.
Image with alt text: The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left-parenthesis 0 comma 0 right-parenthesis, left-parenthesis one-half comma 4 right-parenthesis, and left-parenthesis 1 comma 8 right-parenthesis.
The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages.The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 4 comma 0 right parenthesis, left parenthesis 6 comma 2 right parenthesis, and left parenthesis 8 comma 4 right parenthesis.
Image with alt text: The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 4 comma 0 right parenthesis, left parenthesis 6 comma 2 right parenthesis, and left parenthesis 8 comma 4 right parenthesis.
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The correct graph is the one that shows a line passing through the points (0, 4), (2, 6), and (4, 8).
The graph that represents the relationship between Nick's age and Sara's age is option 3. The graph shows a line passing through the points (0, 0), (1/2, 4), and (1, 8). This represents the fact that Sara's age (y) is half of Nick's age (x).
Based on the given information, we know that Nick is four years older than Sara, which means that there is a constant difference of four years between their ages. We can represent this relationship using a linear equation.
Let x represent Nick's age and y represent Sara's age. Since Nick is four years older than Sara, our equation would be x = y + 4.
To graph this equation, we can choose different values for y and solve for x. Let's choose three values of y (0, 2, and 4) and compute the corresponding values of x.
When y = 0, x = 0 + 4 = 4. So one point on the graph is (4, 0).
When y = 2, x = 2 + 4 = 6. So another point on the graph is (6, 2).
When y = 4, x = 4 + 4 = 8. So the final point on the graph is (8, 4).
Now, we can plot these three points on the graph. The x-axis represents Nick's age, and the y-axis represents Sara's age. Connect the dots to form a line, and we have the graph that represents the relationship between Nick's and Sara's ages.
Looking at the options given:
Option 1: The graph passes through the points (0, 4), (2, 6), and (4, 8). This represents the linear relationship where Nick is four years older than Sara. Therefore, the correct answer is the first option:
The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points (0, 4), (2, 6), and (4, 8).