What is an equation of the line that passes through the points (3,6) and (1,−2)?

To find the equation of the line that passes through the points \((3, 6)\) and \((1, -2)\), we can use the point-slope form of the line equation:

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

First, we need to calculate the slope \(m\) of the line using the formula:

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

Substituting the given points \((x_1, y_1) = (3, 6)\) and \((x_2, y_2) = (1, -2)\):

\[
m = \frac{-2 - 6}{1 - 3} = \frac{-8}{-2} = 4
\]

Now that we have the slope \(m = 4\), we can use the point-slope form with the point \((3, 6)\):

\[
y - 6 = 4(x - 3)
\]

Expanding and simplifying to get the equation in slope-intercept form \(y = mx + b\):

\[
y - 6 = 4x - 12
\]
\[
y = 4x - 6
\]

So, the equation of the line is:

\[
\boxed{y = 4x - 6}
\]

Would you like more details or have any questions?

### Relative Questions:
1. How do you find the slope of a line given two points?
2. What is the difference between point-slope form and slope-intercept form of a line?
3. How do you convert from point-slope form to slope-intercept form?
4. Can you find the equation of a line parallel to \(y = 4x - 6\) passing through another point?
5. What is the significance of the y-intercept in the equation \(y = 4x - 6\)?

### Tip:
Always double-check your calculations when finding the slope to ensure the correct sign and value, as it directly affects the line equation.

What is an equation of the line that passes through the points (3,6) and (1,−2)?

Learn how to find the equation of a line passing through the points (3,6) and (1,-2). This problem covers key algebraic concepts, including calculating the slope and using the point-slope form to derive the line equation. Suitable for students in 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