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

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

Where:
- \( m \) is the slope.
- \( (x_1, y_1) \) is a point on the line.

Given:
- Slope \( m = \frac{3}{5} \)
- Point \( (x_1, y_1) = (-6, -8) \)

Substitute these values into the point-slope form:

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

Simplify the equation:

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

Now, distribute \( \frac{3}{5} \):

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

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

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

To combine \( \frac{18}{5} \) and \( -8 \), convert 8 to a fraction with a denominator of 5:

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

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

Thus, the equation of the line in slope-intercept form is:

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

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the general form of a linear equation?
2. How do you find the y-intercept of a line?
3. What happens to the slope if the line becomes vertical?
4. How can you find the slope between two points?
5. What is the significance of a positive slope?

**Tip:** Always simplify fractions as much as possible when working with equations to avoid errors in calculations.

Learn how to find the equation of a line with a slope of 3/5 passing through the point (-6, -8). This problem explores key algebraic concepts, including the point-slope form and slope-intercept form of linear equations, 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