Write an equation of the line that passes through each pair of points. (2, -2), (3, 2)

To find the equation of the line that passes through the points \((2, -2)\) and \((3, 2)\), follow these steps:

### Step 1: Find the slope of the line
The slope \(m\) of the line is given by the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the given points \((x_1, y_1) = (2, -2)\) and \((x_2, y_2) = (3, 2)\):

\[
m = \frac{2 - (-2)}{3 - 2} = \frac{2 + 2}{1} = \frac{4}{1} = 4
\]

So, the slope \(m = 4\).

### Step 2: Use the point-slope form to find the equation of the line
The point-slope form of a line's equation is:

\[
y - y_1 = m(x - x_1)
\]

Substitute \(m = 4\) and one of the points, say \((2, -2)\):

\[
y - (-2) = 4(x - 2)
\]

Simplify:

\[
y + 2 = 4x - 8
\]

### Step 3: Convert to slope-intercept form (if needed)
To express the equation in slope-intercept form \(y = mx + b\), subtract 2 from both sides:

\[
y = 4x - 10
\]

### Final Answer
The equation of the line that passes through the points \((2, -2)\) and \((3, 2)\) is:

\[
y = 4x - 10
\]

Would you like more details or have any questions? 

Here are some related questions:

1. What is the point-slope form of the equation?
2. How do you convert a line equation to standard form?
3. What is the slope-intercept form of a line?
4. How do you find the slope of a line given two points?
5. Can you determine the y-intercept from the equation \(y = 4x - 10\)?

**Tip:** When finding the slope between two points, remember that it represents how much the y-value changes for a one-unit change in the x-value.

Learn how to write the equation of a line that passes through the points (2, -2) and (3, 2). Follow step-by-step instructions using the slope formula and point-slope form. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation