Math Problem Statement
The table provided contains pairs of (x, y) values: x = [-3, -1, 1, 3, 5] and y = [-2.5, -1.5, -0.5, 0.5, 1.5]. Determine the equation of the line that passes through these points.
Solution
The table you have provided contains pairs of values:
\hline x & -3 & -1 & 1 & 3 & 5 \\ \hline y & -2.5 & -1.5 & -0.5 & 0.5 & 1.5 \\ \hline \end{array}$$ This seems to represent a set of coordinates or points on a graph. The relationship between $$x$$ and $$y$$ appears linear, which means we can likely determine the equation of the line passing through these points. Let's find the equation of the line in the form $$y = mx + b$$, where $$m$$ is the slope and $$b$$ is the y-intercept. ### Step 1: Calculate the slope $$m$$ The slope formula is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Let's use the points $$(-3, -2.5)$$ and $$(5, 1.5)$$: $$m = \frac{1.5 - (-2.5)}{5 - (-3)} = \frac{1.5 + 2.5}{5 + 3} = \frac{4}{8} = 0.5$$ So, the slope $$m = 0.5$$. ### Step 2: Find the y-intercept $$b$$ Using the slope $$m = 0.5$$ and one of the points, say $$(x_1, y_1) = (-3, -2.5)$$, we can substitute into the equation $$y = mx + b$$ to solve for $$b$$: $$-2.5 = 0.5(-3) + b$$ $$-2.5 = -1.5 + b$$ $$b = -2.5 + 1.5 = -1$$ ### Step 3: Equation of the line Thus, the equation of the line is: $$y = 0.5x - 1$$ This equation fits the given data points. Would you like any additional details or have any questions about this solution? Here are some related questions: 1. What is the meaning of the slope in this equation? 2. How can you verify if this line equation fits all the points? 3. What happens to $$y$$ if $$x = 10$$ in this equation? 4. Can you determine the x-intercept of the line from the equation? 5. What is the graphical interpretation of the y-intercept? **Tip**: When working with linear equations, always verify by plugging in a few points to ensure the accuracy of the equation.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Coordinate Geometry
Algebra
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Equation of a line: y = mx + b
Theorems
Slope-Intercept Form
Suitable Grade Level
Grades 8-10
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