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To find the equation of a line that passes through the point (-6, 3) and has a slope of 8, we use the **point-slope form** of a line equation, which is given by:

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

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

Substituting the values:
- \( m = 8 \) (the slope)
- \( (x_1, y_1) = (-6, 3) \) (the point)

The equation becomes:

\[
y - 3 = 8(x + 6)
\]

Now, let's simplify the equation:

\[
y - 3 = 8x + 48
\]

\[
y = 8x + 48 + 3
\]

\[
y = 8x + 51
\]

So, the equation of the line is:

\[
y = 8x + 51
\]

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

1. How do you convert from point-slope form to slope-intercept form?
2. What is the general formula for the slope of a line?
3. How do you find the y-intercept from the equation of a line?
4. How can you verify that a point lies on a given line?
5. How does the slope affect the steepness of a line?

**Tip:** Always double-check your work by plugging the point back into the final equation to ensure it satisfies the line equation.

Write an equation for the line that passes through the point (-6, 3) and has slope of 8.

Learn how to find the equation of a line that passes through the point (-6, 3) and has a slope of 8. The solution involves using the point-slope form and simplifying to slope-intercept form. Suitable for students in Grades 8-10.

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