Math Problem Statement
Write the equation for the table shown:
x | -2 | -1 | 0 | 1 | 2
---|----|----|----|----|----
y | 10 | 7 | 4 | 1 | -2
Solution
The table provided shows the following values:
x & -2 & -1 & 0 & 1 & 2 \\ \hline y & 10 & 7 & 4 & 1 & -2 \\ \end{array}$$ We are tasked with finding the equation that describes the relationship between $$x$$ and $$y$$. ### Step 1: Identify the type of relationship The values of $$y$$ decrease by 3 as $$x$$ increases by 1. This suggests a **linear relationship** of the form: $$y = mx + b$$ Where $$m$$ is the slope and $$b$$ is the y-intercept. ### Step 2: Find the slope ($$m$$) The slope $$m$$ is the change in $$y$$ divided by the change in $$x$$. We can calculate this between any two consecutive points. Let's use the points $$(0, 4)$$ and $$(1, 1)$$: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 4}{1 - 0} = \frac{-3}{1} = -3$$ ### Step 3: Find the y-intercept ($$b$$) To find $$b$$, we substitute the slope $$m = -3$$ and any point from the table into the equation $$y = mx + b$$. Let's use the point $$(0, 4)$$: $$4 = (-3)(0) + b$$ Solving for $$b$$, we get: $$b = 4$$ ### Final Equation: The equation that describes the relationship is: $$y = -3x + 4$$ Would you like further details or explanations? Here are 5 related questions: 1. How do you calculate the slope if the points are not consecutive? 2. What would happen to the equation if the y-intercept was a negative value? 3. How can we verify that this equation works for all points in the table? 4. What are the key characteristics of a linear equation? 5. How can the same method be applied to a non-linear table of values? **Tip:** Always check your equation with multiple points from the table to ensure accuracy!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
y = mx + b
Theorems
Linear Equation Theorem
Suitable Grade Level
Grades 7-10