Subjects algebra

Chocolate Milk Fd889C

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1. The problem asks to find a formula that shows the relationship between the number of teaspoons of chocolate powder $y$ and the amount of milk $x$ in deciliters. 2. From the graph description, the relationship is linear, so we use the formula for a line: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. Identify two points from the graph: $(1,0)$ and $(6,10)$. 4. Calculate the slope $m$: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - 0}{6 - 1} = \frac{10}{5} = 2$$ 5. Since the line passes through $(1,0)$, substitute $x=1$, $y=0$ and $m=2$ into the line equation to find $b$: $$0 = 2 \times 1 + b$$ $$b = 0 - 2 = -2$$ 6. The formula is: $$y = 2x - 2$$ 7. This means for each deciliter of milk, you need 2 teaspoons of chocolate powder minus 2 teaspoons. 8. Check the formula with another point, for example $x=6$: $$y = 2 \times 6 - 2 = 12 - 2 = 10$$ which matches the graph. Final answer: $$y = 2x - 2$$