Subjects algebra

Line Slope 39Efe8

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. The problem asks for the slope of the line and what the slope tells us. 2. The slope of a line is defined as the change in the vertical direction (change in $y$) divided by the change in the horizontal direction (change in $x$): $$\text{slope} = \frac{\Delta y}{\Delta x}$$ 3. From the information given, the slope is 4, which means for every increase of 1 square foot ($x$), the cost or number of stones ($y$) changes by 4. 4. Interpreting the slope: - "You get 4 stones for each square foot" means the slope is 4 stones per square foot. - "The stones cost 4 per square foot" means the cost increases by 4 units per square foot. - "The stones cost 1 for 4 square feet" means the cost per square foot is $\frac{1}{4}$, which contradicts the slope 4, so this is not consistent with the slope. - "You get 4 stones per dollar" means the slope would be stones per dollar, which is the inverse of stones per square foot. 5. The slope represents the rate of change of cost or stones with respect to square feet. Since the slope is 4, it means the cost or stones increase by 4 units for every 1 square foot increase. 6. The slope is the change in cost $y$ when $x$ increases by 1 square foot: $$\text{slope} = \frac{\Delta y}{\Delta x} = 4$$ Final answer: The slope of the line is 4, which means the cost or number of stones increases by 4 for each additional square foot.