# Blue-red paint mixtures in the ratio 2 to 3

A paint company mixed 2 gallons blue paint with 3 gallons red paint and liked the shade of purple that made.
What other quantities of blue and red paint can be mixed to make the exact same shade of purple? Move the slider to see those quantities represented by the lengths of the strips and by the coordinates of the point (x, y) on the line.
If the company knows how many gallons of blue paint they will use (such as 5 gallons blue), then how could they figure out how many gallons of red paint they will need?f Use the strips to explain!
If the company knows how many gallons of red paint they will use (such as 10 gallons red), then how could they figure out how many gallons of blue paint they will need? Use the strips to explain!
Write equations that show how x and y are related and use the strips to explain them!
Note: These equations will also be equations for the line through the points (0,0) and (2,3).

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