Linear Equation from Table Values: Slope-Intercept Form

Math Problem Statement

Write the linear equation that gives the rule for this table.

To determine the linear equation that fits the given table of values, we can analyze the changes in $x$ and $y$ :

The table shows the following pairs:

x & y \\ \hline 5 & 7 \\ 6 & 8 \\ 7 & 9 \\ 8 & 10 \\ \end{array}$$ We observe that as $$x$$ increases by 1, $$y$$ also increases by 1. This suggests that the slope $$m$$ of the linear equation $$y = mx + b$$ is 1. Now, let's find the y-intercept $$b$$. Using one of the points, such as $$(5, 7)$$, we substitute the values into the equation: $$7 = 1(5) + b$$ $$7 = 5 + b$$ $$b = 7 - 5 = 2$$ Thus, the linear equation is: $$y = x + 2$$ If you have any questions or would like more details, feel free to ask! Here are 5 related questions to expand on this concept: 1. How can you determine if a set of points forms a linear relationship? 2. What does the slope of a linear equation represent in real-world contexts? 3. How do you find the slope between two points on a coordinate plane? 4. What happens to the graph of a line when you change the y-intercept? 5. Can the linear equation $$y = x + 2$$ be expressed in a different form? **Tip:** When working with linear equations, always check the change in $$y$$ relative to the change in $$x$$ to find the slope quickly.

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Linear Equations
Algebra

y = mx + b

Slope-Intercept Form

Grades 7-9

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