Math Problem Statement

What is the slope of this chart

What is the slope of this chart?

Solution

To determine the slope of the relationship between xx and yy in this chart, we can use the formula for the slope mm between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), which is:

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

From the table:

x & y \\ \hline 2 & 8 \\ 6 & 28 \\ 10 & 48 \\ 14 & 68 \\ \end{array}$$ We can calculate the slope using any pair of points. Let's choose the first two points: $$(x_1, y_1) = (2, 8)$$ and $$(x_2, y_2) = (6, 28)$$. $$m = \frac{28 - 8}{6 - 2} = \frac{20}{4} = 5$$ Thus, the slope of the line is $$m = 5$$. Would you like further details on this calculation, or do you have any other questions? Here are 5 related questions for further exploration: 1. Can you predict the $$y$$-value when $$x = 20$$ using this slope? 2. How would the slope change if the points were non-linear? 3. What is the equation of the line that passes through the points given in this table? 4. How do you interpret the slope in a real-world context based on the table values? 5. Could you plot this data to visualize the relationship between $$x$$ and $$y$$? **Tip:** Slope is a measure of how much the $$y$$-value changes for each unit increase in the $$x$$-value.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)

Theorems

Linear relationships

Suitable Grade Level

Grades 7-9