Find the Linear Equation from a Table of Values

Math Problem Statement

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

To determine the linear equation that fits the given data in the table, we need to:

Identify two points from the table and use them to find the slope ( $m$ ).
Use the slope to find the y-intercept ( $b$ ) using the slope-intercept form $y = mx + b$ .

The table in the image shows these points:

x & y \\ \hline 5 & 7 \\ 6 & 17 \\ 7 & 27 \\ 8 & 37 \\ \end{array}$$ ### Step 1: Calculate the slope ($$m$$) The slope $$m$$ is calculated using the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using two points, say (5, 7) and (6, 17): $$m = \frac{17 - 7}{6 - 5} = \frac{10}{1} = 10$$ ### Step 2: Use the slope-intercept form The slope-intercept form of a line is: $$y = mx + b$$ Substitute $$m = 10$$ and one of the points (say, $$x = 5$$, $$y = 7$$) to solve for $$b$$: $$7 = 10(5) + b$$ $$7 = 50 + b$$ $$b = 7 - 50 = -43$$ ### Final Equation: The equation of the line is: $$y = 10x - 43$$ Would you like more details on any part of this process? Here are five related questions: 1. How do you calculate the slope between any two points? 2. How do you use the slope and a point to find the y-intercept? 3. What other methods can be used to find the equation of a line? 4. What does the slope represent in real-world scenarios? 5. Can a table of values represent a non-linear equation? **Tip:** Always double-check the calculation of your slope by using different pairs of points.

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Algebra
Linear Equations
Slope-Intercept Form

Slope formula m = (y2 - y1) / (x2 - x1)
Slope-Intercept form y = mx + b

Grades 8-10

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Linear Equation from a Table of Values: Slope-Intercept Form