Math Problem Statement
Which equation represents the linear relationship between x and y
Solution
To determine which equation represents the linear relationship between and , we can analyze the table of values shown in the image:
\hline x & 1 & 2 & 3 & 4 \\ \hline y & 6 & 9 & 12 & 15 \\ \hline \end{array}$$ To find the equation that represents the relationship between $$x$$ and $$y$$, we need to observe how $$y$$ changes as $$x$$ increases. 1. Calculate the slope ($$m$$) of the line using any two points. Let's use the points $$(1, 6)$$ and $$(2, 9)$$: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - 6}{2 - 1} = \frac{3}{1} = 3$$ 2. Now that we have the slope $$m = 3$$, we can use the point-slope form of the equation of a line, $$y = mx + b$$, to find the y-intercept $$b$$. Using the point $$(1, 6)$$: $$6 = 3(1) + b \implies b = 6 - 3 = 3$$ So the equation of the line is: $$y = 3x + 3$$ Looking at the options in the image, the correct equation that represents the linear relationship between $$x$$ and $$y$$ is: $$\boxed{y = 3x + 3}$$ Let me know if you want further details or explanations! Here are some related questions: 1. How do you determine the slope from a table of values? 2. What does the y-intercept represent in a linear equation? 3. How can you verify that a linear equation correctly represents the data in a table? 4. What is the general form of a linear equation? 5. How can you interpret the meaning of slope in real-life scenarios? **Tip:** When working with linear relationships, always check if the difference in $$y$$ values divided by the difference in $$x$$ values remains constant—this confirms that the relationship is indeed linear.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Point-Slope Form
Formulas
Slope formula
Point-slope form of a line
Theorems
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Suitable Grade Level
Grades 7-9