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To write the equation of a line we need to know 1. The slope 2. One point on the line

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X Y 5 5 -5 (-, ) Given a slope and a point on the line. Use the POINT-SLOPE form ! y – y 1 = m ( x – x 1 )

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X Y 5 5 -5 (-, ) Use the POINT-SLOPE form ! y – y 1 = m ( x – x 1 ) Find the SLOPE Given 2 points on the line

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X Y 5 5 -5 (-, ) y = mx + b Use SLOPE-INTERCEPT form ! Given the y-intercept * Note: We will also need either the slope (m) or another point on the line (x, y) in order to find the equation.

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X Y 5 5 -5 (-, ) Two variables x and y vary directly (are directly proportional) if the ratio of y to x is always the same. The ratio of dependent to independent is constant. If two quantities always vary at the same rate, they vary directly. (they are directly proportional) y/x = k

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X Y 5 5 -5 (-, ) y/x = k Then y = kx the constant of variation Dependent Variable Independent Variable = K

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X Y 5 5 -5 (-, ) The sides of similar triangles are in proportion. In other words, the ratio of any large side to the corresponding small side is always the same (constant) They vary directly! 4 15 x 12

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X Y 5 5 -5 (-, ) To create a model for direct variation, start with Then use the known information to find the constant of variation! y = kx 4 15 x 12 12 = k(4) k=3

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X Y 5 5 -5 (-, ) Re-write the equation : y = 3x 4 15 x 12 Now use this equation to find other values… (x, 15) what is x? 15 = 3x 5=x

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X Y 5 5 -5 (-, ) The number of chickens varies directly as the number of eggs. Farmer Ralfi has 220 chickens and 36 eggs. If John wants to be a farmer like Ralfi and he buys 40 chickens, how many eggs can he expect?

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Direct Variation We say that two positive quantities x and y vary directly if an increase in one causes a proportional increase in the other. In this case,

Direct Variation We say that two positive quantities x and y vary directly if an increase in one causes a proportional increase in the other. In this case,

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