Graph the line that passes through the points left parenthesis, 8, comma, minus, 3, right parenthesis(8,−3) and left parenthesis, 2, comma, minus, 3, right parenthesis(2,−3) and determine the equation of the line.


To graph the line and determine its equation, let's follow these steps:

### 1. Find the slope of the line:

Given two points \((8, -3)\) and \((2, -3)\), we can calculate the slope using the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the coordinates:
\[
m = \frac{-3 - (-3)}{2 - 8} = \frac{0}{-6} = 0
\]

Since the slope \(m = 0\), this indicates the line is **horizontal**.

### 2. Write the equation of the line:

For a horizontal line, the equation is always of the form:
\[
y = c
\]
where \(c\) is the constant value of \(y\) for all points on the line.

In this case, since \(y = -3\) for both points, the equation of the line is:
\[
y = -3
\]

### 3. Graph the line:

The graph is a horizontal line passing through \(y = -3\) on the \(y\)-axis. Every point on this line will have \(y = -3\), regardless of the \(x\)-value.

---

Would you like me to plot the graph for you?

### Questions:
1. What is the general form of the equation for a horizontal line?
2. Can a horizontal line ever have a non-zero slope?
3. How does a vertical line's equation differ from a horizontal line's?
4. What does a slope of zero represent in terms of real-life applications?
5. How would the equation change if the points were on a vertical line?

**Tip:** When the slope of a line is zero, it indicates that the line is horizontal and the \(y\)-coordinate remains constant for all \(x\)-values.

Graph the line that passes through the points (8,−3) and (2,−3) and determine the equation of the line.

Learn how to graph the line passing through the points (8,-3) and (2,-3) and determine the equation. This tutorial covers key concepts in coordinate geometry, including calculating the slope and writing the equation of a horizontal line. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation