A line has an equation 3x-7y=14. Write the equation in slope-intercept form.

To convert the equation \(3x - 7y = 14\) to slope-intercept form (\(y = mx + b\)), follow these steps:

1. **Isolate** the \(y\) term on one side of the equation:
   \[
   -7y = -3x + 14
   \]
   
2. **Divide** both sides of the equation by \(-7\) to solve for \(y\):
   \[
   y = \frac{-3x + 14}{-7}
   \]
   
3. **Simplify** the equation:
   \[
   y = \frac{3}{7}x - 2
   \]

So, the slope-intercept form of the equation is:
\[
y = \frac{3}{7}x - 2
\]

In this form, the slope (\(m\)) is \(\frac{3}{7}\), and the y-intercept (\(b\)) is \(-2\).

Would you like further details or have any questions? Here are some related questions:

1. How do you find the slope of a line given two points?
2. What is the significance of the y-intercept in a linear equation?
3. How do you convert a slope-intercept form equation back to standard form?
4. How can you graph a line using its slope and y-intercept?
5. What is the general process to find the equation of a line parallel to a given line?

**Tip:** To quickly identify the slope and y-intercept of a line, always try to rearrange the equation into the slope-intercept form, \(y = mx + b\).

Learn how to convert the linear equation 3x - 7y = 14 to slope-intercept form (y = mx + b) with detailed steps and explanations. This problem covers linear equations and the slope-intercept form, suitable for students in 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