Graph Set A = {(x, y): (2, -2), (4, -1), (6, 0), . . .}

To graph Set A, we first recognize that the set consists of points of the form \((x, y)\), where the given points are \((2, -2)\), \((4, -1)\), \((6, 0)\), and likely follow a specific pattern.

Looking at the x-values: \(2, 4, 6, \dots\), they increase by 2 each time.
Looking at the y-values: \(-2, -1, 0, \dots\), they increase by 1 each time.

Thus, the next few points are:
\[
(8, 1), (10, 2), \dots
\]

This suggests a linear relationship between \(x\) and \(y\).

### To find the equation of the line:
1. Pick two points, say \((2, -2)\) and \((4, -1)\).
2. The slope \(m\) is calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - (-2)}{4 - 2} = \frac{1}{2}
\]
3. Using the point-slope form of a line, \(y - y_1 = m(x - x_1)\), and the point \((2, -2)\):
\[
y - (-2) = \frac{1}{2}(x - 2)
\]
4. Simplifying:
\[
y + 2 = \frac{1}{2}(x - 2) \quad \Rightarrow \quad y = \frac{1}{2}x - 3
\]

Thus, the equation of the line is \(y = \frac{1}{2}x - 3\).

Now, to **graph Set A**, plot the points and draw the line \(y = \frac{1}{2}x - 3\).

Would you like me to generate the graph, or do you need further clarification?

### Related Questions:
1. How do you graph points on a coordinate plane?
2. What is the significance of the slope in the equation of a line?
3. How do you determine the pattern in a set of points?
4. Can you explain the point-slope form of a line equation in more detail?
5. How would the graph change if the slope was negative?

**Tip:** Always look for patterns in both x- and y-values when identifying a trend in a set of points.

Learn how to graph a set of points following a linear pattern, including the solution and equation of the line. Understand key concepts like slope calculation and point-slope form. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation