Math Problem Statement
(a) Draw a scatter plot of the data. (b) Find the equation of the line, in slope-intercept form, containing the points (2.3,6.6) and (1.8,6.6). (c) Graph the line found in part (b) on the scatter plot. x: [1.2, 1.8, 2.3, 3.5, 4.1], y: [8.2, 6.6, 6.6, 5.7, 2.6]
Solution
Let's work through the steps based on the image:
(a) Choose the correct scatter plot:
The table of values provided is:
\hline x & y \\ \hline 1.2 & 8.2 \\ 1.8 & 6.6 \\ 2.3 & 6.6 \\ 3.5 & 5.7 \\ 4.1 & 2.6 \\ \hline \end{array}$$ Looking at the scatter plots: - Scatter plot **A** correctly reflects the points. - The values of $$x$$ range from about 1.2 to 4.1. - The values of $$y$$ range from 2.6 to 8.2. - Scatter plots **B**, **C**, and **D** do not match the data, either in scale or positioning. Thus, **scatter plot A** is the correct answer. --- ### (b) Find the equation of the line, in slope-intercept form: You're asked to find the equation of a line passing through the points $$(2.3, 6.6)$$ and $$(1.8, 6.6)$$. The slope $$m$$ of a line passing through two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is calculated by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ For the points $$(2.3, 6.6)$$ and $$(1.8, 6.6)$$: $$m = \frac{6.6 - 6.6}{2.3 - 1.8} = \frac{0}{0.5} = 0$$ Since the slope is 0, the line is horizontal, and the equation of the line is simply: $$y = 6.6$$ This is the equation in slope-intercept form. --- Would you like further clarification on this, or would you like to discuss the remaining parts of the question? Below are a few related questions for additional practice: 1. What would the equation of the line be if the slope was non-zero? 2. How do you graph a vertical line using only the $$x$$-coordinates? 3. Can you determine the slope if given two points where $$y_2 \neq y_1$$? 4. How would you determine the slope if the coordinates included decimal values with negative signs? 5. How can you derive the intercept of a line using its equation? **Tip**: When the slope is 0, it means the line is horizontal, and all points on the line have the same $$y$$-value.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Graphing
Linear Equations
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + b
Theorems
Properties of linear equations
Slope of horizontal lines
Suitable Grade Level
Grades 8-10
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