**Understanding Proportional Relationships and Unit Rates** **Problem Statement:** Sasha wrote the equation \(y = 6x\). Which graph shows a proportional relationship with a greater unit rate than Sasha's equation? **Graphs Overview:** There are four graphs (A, B, C, and D) displayed. Each graph plots \(y\) versus \(x\) on a grid. The unit rates for the functions represented by these graphs should be compared to determine which one has a greater unit rate than the equation \(y = 6x\), where the unit rate is 6. **Graph A:** - \(y\)-axis ranges from 0 to 20. - \(x\)-axis ranges from 0 to 10. - The line passes through points (0,0) and (3,18). - The unit rate (slope) is 6. **Graph B:** - \(y\)-axis ranges from 0 to 20. - \(x\)-axis ranges from 0 to 10. - The line passes through points (0,0) and (2,20). - The unit rate (slope) is 10. **Graph C:** - \(y\)-axis ranges from 0 to 20. - \(x\)-axis ranges from 0 to 10. - The line passes through points (0,0) and (6,6). - The unit rate (slope) is 1. **Graph D:** - \(y\)-axis ranges from 0 to 20. - \(x\)-axis ranges from 0 to 10. - The line passes through points (0,0) and (4,12). - The unit rate (slope) is 3. **Conclusion:** - Graph B shows a proportional relationship with a unit rate of 10, which is greater than Sasha's unit rate of 6 in the equation \(y = 6x\).

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.