To find the equation of a line with slope \( \frac{3}{5} \) that passes through the point \( (-6, -8) \), we use the point-slope form of the equation of a line:

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

Where:
- \( m \) is the slope (\( \frac{3}{5} \)),
- \( (x_1, y_1) \) is the point the line passes through (\( (-6, -8) \)).

Substituting these values into the formula:

\[
y - (-8) = \frac{3}{5}(x - (-6))
\]

Simplifying the equation:

\[
y + 8 = \frac{3}{5}(x + 6)
\]

Now distribute the slope:

\[
y + 8 = \frac{3}{5}x + \frac{18}{5}
\]

To isolate \( y \), subtract 8 from both sides:

\[
y = \frac{3}{5}x + \frac{18}{5} - 8
\]

Convert 8 to a fraction with a denominator of 5:

\[
y = \frac{3}{5}x + \frac{18}{5} - \frac{40}{5}
\]

Now simplify:

\[
y = \frac{3}{5}x - \frac{22}{5}
\]

So, the equation of the line is:

\[
y = \frac{3}{5}x - \frac{22}{5}
\]

Would you like more details on how the slope-intercept form works, or do you have any further questions?

Here are 5 related questions to explore:
1. How do you convert a line equation from point-slope form to slope-intercept form?
2. What is the importance of the slope in a line equation?
3. How do you calculate the slope given two points?
4. What is the meaning of the y-intercept in a linear equation?
5. How can you determine if two lines are parallel or perpendicular?

**Tip:** The point-slope form is especially useful when you're given a point and the slope, as it simplifies the process of finding the equation of a line.

This problem demonstrates how to find the equation of a line with a slope of 3/5 passing through the point (-6, -8). Using the point-slope form of the equation, this detailed solution explains each step to convert it into slope-intercept form, 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