What is the equation of the line that passes through the point left parenthesis, minus, 6, comma, 3, right parenthesis(−6,3) and has a slope of minus, start fraction, 4, divided by, 3, end fraction− 
3
4
​
 ?

To find the equation of a line passing through a given point \((-6, 3)\) with a slope of \(-\frac{4}{3}\), we can use the **point-slope form** of a linear equation:

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

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

Given:
- Slope \(m = -\frac{4}{3}\)
- Point \((x_1, y_1) = (-6, 3)\)

Substituting these values into the point-slope form:

\[
y - 3 = -\frac{4}{3}(x + 6)
\]

Now, let's simplify this equation:

1. Distribute \(-\frac{4}{3}\) across \((x + 6)\):
   \[
   y - 3 = -\frac{4}{3}x - 8
   \]

2. Add 3 to both sides to solve for \(y\):
   \[
   y = -\frac{4}{3}x - 8 + 3
   \]
   \[
   y = -\frac{4}{3}x - 5
   \]

So, the equation of the line is:

\[
y = -\frac{4}{3}x - 5
\]

Would you like more details on how this was solved?

### 5 Related Questions:
1. What is the point-slope form of a linear equation, and how is it derived?
2. How do you convert the point-slope form to slope-intercept form?
3. What are other forms of a linear equation, and how do they differ?
4. How can you verify if a given point lies on a particular line?
5. How does the slope of a line relate to its steepness and direction?

### Tip:
Always simplify your equation as much as possible to present the answer in its most straightforward form, usually slope-intercept form \(y = mx + b\).

What is the equation of the line that passes through the point (−6, 3) and has a slope of −4/3?

Find the equation of the line passing through the point (-6, 3) with a slope of -4/3. This step-by-step guide covers the point-slope form and converting to slope-intercept form, providing a clear understanding for students in Grades 8-10.

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