Find an equation of the line with slope m that passes through the given point (-5,-2), m=4/5

To find the equation of a line with a given slope \( m \) and passing through a specific point \((x_1, y_1)\), we use the point-slope form of the equation of a line:

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

Given:
- Slope \( m = \frac{4}{5} \)
- Point \((-5, -2)\)

Substitute the values into the point-slope form:

\[
y - (-2) = \frac{4}{5}(x - (-5))
\]

Simplify the equation:

\[
y + 2 = \frac{4}{5}(x + 5)
\]

Distribute \( \frac{4}{5} \) on the right side:

\[
y + 2 = \frac{4}{5}x + \frac{4}{5} \times 5
\]

\[
y + 2 = \frac{4}{5}x + 4
\]

Finally, subtract 2 from both sides to get the equation in slope-intercept form \( y = mx + b \):

\[
y = \frac{4}{5}x + 4 - 2
\]

\[
y = \frac{4}{5}x + 2
\]

So, the equation of the line is:

\[
y = \frac{4}{5}x + 2
\]

Would you like any further details or have any questions?

Here are some related questions you might find helpful:
1. How do you convert the equation of a line from point-slope form to standard form?
2. What is the significance of the y-intercept in a linear equation?
3. How do you find the equation of a line parallel to a given line?
4. How can you determine if two lines are perpendicular?
5. What is the equation of a line passing through two given points?

**Tip:** When given a point and a slope, always start with the point-slope form to easily derive the line's equation.

Learn how to find the equation of a line with a given slope and passing through a specific point (-5, -2). Step-by-step solution provided, covering key concepts of linear equations and point-slope form. Suitable for Grades 7-9.

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