What is the equation of the line that passes through the point left parenthesis, minus, 1, comma, 6, right parenthesis(−1,6) and has a slope of 11?

To find the equation of the line that passes through the point \((-1, 6)\) and has a slope of \(11\), we can use the point-slope form of the equation of a line:

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

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

Substituting the given values into the equation:

- \( x_1 = -1 \)
- \( y_1 = 6 \)
- \( m = 11 \)

\[
y - 6 = 11(x - (-1))
\]

Simplify the equation:

\[
y - 6 = 11(x + 1)
\]

Distribute the \(11\) on the right side:

\[
y - 6 = 11x + 11
\]

Finally, add 6 to both sides to get the equation in slope-intercept form \( y = mx + b \):

\[
y = 11x + 17
\]

So, the equation of the line is:

\[
\boxed{y = 11x + 17}
\]

Would you like more details or have any questions?

Here are 8 related questions you might find interesting:
1. How do you convert the equation of a line from point-slope form to slope-intercept form?
2. What is the general form of the equation of a line, and how does it relate to the slope-intercept form?
3. How do you find the slope of a line given two points?
4. What is the significance of the slope in the context of a line?
5. How do you determine if two lines are parallel, perpendicular, or neither?
6. How would you find the y-intercept if the slope and a point on the line are given?
7. How do you write the equation of a line parallel to a given line that passes through a specific point?
8. How do you find the equation of a line given its graph?

**Tip:** Always check your final equation by substituting the given point back into it to verify correctness.

Learn how to find the equation of a line passing through the point (-1, 6) with a slope of 11. This problem involves using the point-slope form of a linear equation and is suitable for students in Grades 7-9.

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