 Write the equation of the line passing through the points (2, 1) and (0, −5).

To find the equation of the line passing through the points \((2, 1)\) and \((0, -5)\), follow these steps:

### Step 1: Find the slope (\(m\)) of the line
The formula for the slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute \((x_1, y_1) = (2, 1)\) and \((x_2, y_2) = (0, -5)\):
\[
m = \frac{-5 - 1}{0 - 2} = \frac{-6}{-2} = 3
\]

### Step 2: Use the point-slope form of the equation
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
Using the slope \(m = 3\) and one of the points, say \((2, 1)\):
\[
y - 1 = 3(x - 2)
\]

### Step 3: Simplify to slope-intercept form (\(y = mx + b\))
Expand and simplify:
\[
y - 1 = 3x - 6
\]
\[
y = 3x - 5
\]

### Final Equation
The equation of the line is:
\[
y = 3x - 5
\]

Would you like a step-by-step explanation or further details?  

Here are 5 questions to expand your understanding:  
1. How do you determine the slope of a line given two points?  
2. What is the difference between point-slope and slope-intercept form?  
3. Can you find the equation of a line parallel to this one passing through a different point?  
4. How would the equation change if the points were swapped?  
5. How do you graph this equation on a coordinate plane?  

**Tip:** Always simplify fractions when calculating the slope for a cleaner equation.

Write the equation of the line passing through the points (2, 1) and (0, −5).

Learn how to find the equation of the line passing through the points (2, 1) and (0, −5). This problem includes the calculation of slope, the use of point-slope form, and the conversion to slope-intercept 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