Math Problem Statement
answer
Find the slope using the table of points provided (x, y): (3, 7), (1, 4), (-5, -5), (-9, -11).
Solution
The table you provided gives a set of coordinates:
x & y \\ \hline 3 & 7 \\ 1 & 4 \\ -5 & -5 \\ -9 & -11 \\ \end{array}$$ To find the slope ($$m$$) between any two points, we use the slope formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Let's calculate the slope between two points. I'll choose the first two points: $$(3, 7)$$ and $$(1, 4)$$. $$m = \frac{4 - 7}{1 - 3} = \frac{-3}{-2} = \frac{3}{2}$$ So, the slope between these two points is $$\frac{3}{2}$$. If you want, we can verify this slope by calculating between different points or check for consistency with the other pairs. Would you like more details or have any further questions? Here are five questions to consider for deeper understanding: 1. What is the formula to calculate the slope between two points? 2. How can you tell if a set of points has the same slope? 3. Can you determine the equation of the line from this slope and one of the points? 4. How does the slope help in understanding the relationship between $$x$$ and $$y$$? 5. What happens to the slope when the $$x$$ values are the same in two points? **Tip:** When points lie on the same straight line, the slope calculated between any two points will always be the same.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope Calculation
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Theorems
Slope between two points
Suitable Grade Level
Grades 7-9