Subjects algebra

Proportional Relationship A8A7A1

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1. **Stating the problem:** We are given a graph of a proportional relationship passing through the origin and the point approximately $(8, 1050)$. We need to find the equation of this proportional relationship. 2. **Formula used:** For proportional relationships, the equation is of the form $$y = kx$$ where $k$ is the constant of proportionality (the slope). 3. **Finding the constant $k$:** Since the line passes through $(8, 1050)$, substitute these values into the equation: $$1050 = k \times 8$$ 4. **Solving for $k$:** $$k = \frac{1050}{8}$$ 5. **Simplify the fraction:** $$k = \frac{\cancel{1050}}{\cancel{8}} = 131.25$$ 6. **Final equation:** $$y = 131.25x$$ This means for every increase of 1 in $x$, $y$ increases by 131.25, confirming the proportional relationship.