1. **Problem Statement:** We are given two sets of data representing the relationship between the number of hours worked and the amount charged by two lawn care services: Susan's Lawn Care (table) and Jim's Lawn Care (graph). 2. **Goal:** Understand the linear relationship between hours worked and amount charged for both services. 3. **Formula for Linear Relationship:** The amount charged $y$ is related to hours worked $x$ by a linear equation: $$y = mx + b$$ where $m$ is the rate (slope) and $b$ is the fixed charge (y-intercept). 4. **Susan's Lawn Care Analysis:** - From the table, pick two points: $(2,48)$ and $(3,72)$. - Calculate slope $m$: $$m = \frac{72 - 48}{3 - 2} = \frac{24}{1} = 24$$ - Check if $b=0$ by substituting $x=2$: $$48 = 24 \times 2 + b \Rightarrow b = 48 - 48 = 0$$ - Equation for Susan's Lawn Care: $$y = 24x$$ 5. **Jim's Lawn Care Analysis:** - Given points: $(1,20)$ and $(6,140)$. - Calculate slope $m$: $$m = \frac{140 - 20}{6 - 1} = \frac{120}{5} = 24$$ - Find $b$ using point $(1,20)$: $$20 = 24 \times 1 + b \Rightarrow b = 20 - 24 = -4$$ - Equation for Jim's Lawn Care: $$y = 24x - 4$$ 6. **Interpretation:** Both services charge at a rate of 24 dollars per hour. Susan's Lawn Care has no fixed fee, while Jim's Lawn Care has a fixed fee of -4 dollars (which may indicate a discount or adjustment). **Final answers:** - Susan's Lawn Care: $$y = 24x$$ - Jim's Lawn Care: $$y = 24x - 4$$