Math Problem Statement
The table of values represents a linear function, find the equation of the line.
Solution
The table provided shows values of and corresponding values of . It appears that the table represents a linear function. Let's analyze it to find the equation of the line.
The table gives:
\hline x & f(x) \\ \hline 3 & 7 \\ 4 & 9 \\ 5 & 11 \\ 6 & 13 \\ \hline \end{array}$$ ### Step 1: Find the slope ($$m$$) The slope of a line can be calculated using the formula: $$m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$$ Using the points $$(3, 7)$$ and $$(4, 9)$$: $$m = \frac{9 - 7}{4 - 3} = \frac{2}{1} = 2$$ So, the slope of the line is $$m = 2$$. ### Step 2: Find the y-intercept ($$b$$) We use the slope-intercept form of the equation of a line: $$f(x) = mx + b$$ Substituting one of the points, say $$(3, 7)$$, into this equation: $$7 = 2(3) + b$$ $$7 = 6 + b$$ $$b = 1$$ ### Final Equation of the Line: $$f(x) = 2x + 1$$ Would you like further details or clarifications on this? Here are 5 additional related questions: 1. How do you calculate the slope if you have two points on a line? 2. What is the significance of the slope in a linear equation? 3. Can you use a different point to calculate the y-intercept and check if the result is the same? 4. How would you graph this linear equation on a coordinate plane? 5. What happens to the slope and y-intercept if you modify the values in the table? **Tip:** Always ensure the slope is consistent across all pairs of points in a table before concluding that the function is linear.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Algebra
Slope-Intercept Form
Formulas
Slope formula: m = (f(x2) - f(x1)) / (x2 - x1)
Slope-intercept form: f(x) = mx + b
Theorems
Linear Equation
Suitable Grade Level
Grades 8-10