The Coordinate Plane Unit Test
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Question
Use the image to answer the question.
A graph plots cups of yogurt versus slices of mango on x and y axes, respectively, with the x-axis ranging from 0 to 10 in increments of 1 and the y-axis ranging from 0 to 80 in increments of 8. Details of the plots are as follows: left parenthesis 2 comma 16 right parenthesis; left parenthesis 4 comma 32 right parenthesis; and left parenthesis 6 comma 48 right parenthesis.
How many slices of mango are needed for 10 cups of yogurt?
(1 point)
slices of mango
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To find the number of slices of mango needed for 10 cups of yogurt, we need to find the y-coordinate when the x-coordinate is 10.
Since the x-axis ranges from 0 to 10 in increments of 1, when x = 10, the corresponding y-coordinate can be found by intersecting the vertical line passing through x = 10 with the plots on the graph.
Looking at the plots on the graph, we can see that when x = 2, y = 16; when x = 4, y = 32; and when x = 6, y = 48.
Thus, we can assume that the points between (2,16) and (4,32), and between (4,32) and (6,48) follow a linear pattern.
Let's calculate the slope between the first two points:
slope = (y2 - y1) / (x2 - x1) = (32 - 16) / (4 - 2) = 16 / 2 = 8.
The equation of the line passing through (2,16) and (4,32) is:
y - y1 = m(x - x1),
where m represents the slope and (x1, y1) represents one of the points.
Using the point (2,16):
y - 16 = 8(x - 2),
y - 16 = 8x - 16,
y = 8x.
Now, let's calculate the slope between the second two points:
slope = (y2 - y1) / (x2 - x1) = (48 - 32) / (6 - 4) = 16 / 2 = 8.
The equation of the line passing through (4,32) and (6,48) is:
y - y1 = m(x - x1),
where m represents the slope and (x1, y1) represents one of the points.
Using the point (4,32):
y - 32 = 8(x - 4),
y - 32 = 8x - 32,
y = 8x.
Since both equations have the same form, we can assume that the relationship between the number of cups of yogurt and slices of mango is described by a linear equation: y = 8x.
To find the number of slices of mango needed for 10 cups of yogurt, we can substitute x = 10 into the equation:
y = 8(10),
y = 80.
Therefore, 80 slices of mango are needed for 10 cups of yogurt.