Math Problem Statement
Find the equation of the linear function represented by the table below in slope-intercept form.
xy
11
33
2
7
3
11
4
15
Solution
To find the equation of the linear function in slope-intercept form, we need to determine the slope and the y-intercept of the line, using the given points in the table:
\hline x & y \\ \hline 1 & 1 \\ 2 & 3 \\ 3 & 7 \\ 4 & 11 \\ \hline \end{array}$$ ### Step 1: Calculate the slope $$m$$ The slope $$m$$ of a linear function can be calculated using the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Let's take two points from the table, say $$(2, 3)$$ and $$(3, 7)$$: $$m = \frac{7 - 3}{3 - 2} = \frac{4}{1} = 4$$ So, the slope $$m = 4$$. ### Step 2: Use the slope-intercept form $$y = mx + b$$ Now that we know $$m = 4$$, we substitute it into the slope-intercept form equation: $$y = 4x + b$$ ### Step 3: Solve for $$b$$ (the y-intercept) To find $$b$$, we use one of the points from the table. Let's use $$(1, 1)$$: $$1 = 4(1) + b$$ $$1 = 4 + b$$ $$b = 1 - 4 = -3$$ ### Final Equation Now that we have both the slope $$m = 4$$ and the y-intercept $$b = -3$$, the equation of the linear function is: $$y = 4x - 3$$ --- Would you like more details on any step or have any questions? Here are 5 related questions to deepen understanding: 1. What is the general form of a linear equation, and how does it differ from slope-intercept form? 2. Can you find the slope and y-intercept if given two other points from the table? 3. How would the equation change if we only knew one point and the slope? 4. What does the slope of 4 tell us about the behavior of the line? 5. How can you graph this linear function using the equation? **Tip:** When working with linear equations, always start by identifying the slope first, as it tells you how steep the line is and helps in quickly writing the equation.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Functions
Slope-Intercept Form
Formulas
Slope formula m = (y2 - y1) / (x2 - x1)
Slope-intercept form y = mx + b
Theorems
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Suitable Grade Level
Grades 8-10