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There is a proportional relationship between the weight and total cost of a bag of cherries. One bag weighs 2.1 pounds and costs $7.98. Another bag weighs 2.8 pounds and costs $10.64.

Describe how you would graph the proportional relationship. (4 points)
( I keep getting answers that make no sense so sorry for the spam.)

User Jtrick
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1 Answer

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Explanation:

you need to have or create a coordinate grid with x and y coordinate axis (crossing each other at a right angle in the center).

you got 2 data points (2 bags of cherries with their weight and price).

a proportional (or linear) relationship is graphed as a straight line that goes through these 2 points.

the x axis (left-right) stands for the weight, the y-axis (up-down) stands for the price.

we see, when the weight goes up by 0.7 pounds (from 2.1 to 2.8), the price goes up by $2.66.

the slope of the line is

y-diff / x-diff = 2.66/0.7 = 3.8 = 38/10 = 19/5

the general equation of a line is

y = ax + b

a being the slope, b being the y-intercept (the y-value when x = 0).

we know now

y = 19/5 x + b

we use the coordinates of one point to get b :

7.98 = 19/5 × 2.1 + b = 7.98 + b

b = 0

our line equation is therefore

y = 19/5 x

since the original data coordinates are not nice numbers for a grid of whole numbers, let's find now 2 good points to mark on the grid and draw the line.

one point : x = 0. that gives us y = 0. so, (0, 0).

another point : x = 5. that gives us y = 19.

so, mark the points on your coordinate grid

(0, 0) means x = 0, y = 0 (the point where the 2 coordinate axis cross).

(5, 19) means x = 5, y = 19. or if you don't have that much space in the y direction, we can divide both coordinates in half (we can do that because this is proportional or linear) and get

(2.5, 9.5), and you mark this point instead (you can mark half-units with sufficient accuracy).

and then you draw a line through both points (extending beyond the points).

User Marko Kevac
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