Math Problem Statement
Find the equation of the linear function represented by the table below in slope-intercept form.
Solution
The table provided lists the values for and , which we can use to determine the linear equation in slope-intercept form, , where is the slope and is the y-intercept.
Given dataThe table provided lists the values for and , which we can use to determine the linear equation in slope-intercept form, , where is the slope and is the y-intercept.
Given
x & y \\ \hline 0 & 2 \\ 2 & 4 \\ 4 & 6 \\ \end{array}$$ ### Step 1: Calculate the slope ($$m$$) The formula for the slope between two points, $$(x_1, y_1)$$ and $$(x_2, y_2)$$, is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points $$(0, 2)$$ and $$(2, 4)$$: $$m = \frac{4 - 2}{2 - 0} = \frac{2}{2} = 1$$ ### Step 2: Determine the y-intercept ($$b$$) Since the y-intercept is where $$x = 0$$, from the table, when $$x = 0$$, $$y = 2$$. Therefore, $$b = 2$$. ### Step 3: Write the equation Now that we have the slope $$m = 1$$ and the y-intercept $$b = 2$$, the equation is: $$y = 1x + 2 \quad \text{or simply} \quad y = x + 2$$ Thus, the equation of the linear function is $$y = x + 2$$. Would you like any further details or explanations on this process? --- Here are 5 related questions to expand on this concept: 1. How would you find the equation if the slope was a negative value? 2. What happens to the graph of a line if the y-intercept is 0? 3. Can a table represent a non-linear function? How can you tell from the values? 4. How would you solve for $$x$$ given a specific value for $$y$$ in this equation? 5. How can you use this equation to predict $$y$$-values for any $$x$$-value? **Tip**: When working with a table, check if the change in $$y$$ is consistent for equal changes in $$x$$ to confirm it's a linear function.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
Slope formula
Slope-Intercept Equation
Suitable Grade Level
Grades 8-10