Math Problem Statement
Write the linear equation that gives the rule for this table: (4, 1), (5, 2), (6, 3), (7, 4).
Solution
To find the linear equation that matches the table provided, we need to determine the relationship between the values of and .
Here is the table:
x & y \\ \hline 4 & 1 \\ 5 & 2 \\ 6 & 3 \\ 7 & 4 \\ \end{array}$$ ### Step 1: Determine the slope $$m$$ The slope $$m$$ of the linear equation $$y = mx + b$$ is calculated using the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Let's use the first two points from the table: $$(4, 1)$$ and $$(5, 2)$$. $$m = \frac{2 - 1}{5 - 4} = \frac{1}{1} = 1$$ So, the slope $$m = 1$$. ### Step 2: Find the y-intercept $$b$$ Now, we'll use one of the points to find the y-intercept $$b$$. We can use the point $$(4, 1)$$: $$y = mx + b$$ Substituting the values: $$1 = 1(4) + b$$ $$1 = 4 + b$$ $$b = 1 - 4 = -3$$ ### Step 3: Write the equation The linear equation that represents the table is: $$y = x - 3$$ If you have any more questions or need further details, feel free to ask! --- Here are some related questions you might consider: 1. What is the significance of the slope in a linear equation? 2. How would the equation change if the y-intercept were positive? 3. How can you verify if a given point lies on the line $$y = x - 3$$? 4. What would be the equation if the slope were doubled? 5. How can you graph the equation $$y = x - 3$$ using the slope and y-intercept? **Tip:** Always double-check your calculations, especially when determining the slope and intercept, to ensure accuracy.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
y = mx + b
Theorems
Slope formula m = (y2 - y1) / (x2 - x1)
Suitable Grade Level
Grades 7-8