(-1,6);y=9x-5 write the equation in slope intercept form 

To write the equation of a line in slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), we can follow these steps:

### 1. Use the given point \((-1, 6)\) and the equation of the line \( y = 9x - 5 \).
The slope \( m \) is already provided as 9. We just need to check if the given point lies on the line or if we are asked to modify the line equation to fit that point.

Let’s plug the point \((-1, 6)\) into the equation \( y = 9x - 5 \) and check if it satisfies the equation:

\[
y = 9(-1) - 5 = -9 - 5 = -14
\]

But the given y-value is 6, not -14. This means that \((-1, 6)\) is not a point on the line \( y = 9x - 5 \).

### 2. Equation of the line passing through the point \((-1, 6)\)
To write the equation of a line that passes through the point \((-1, 6)\) with a slope of 9, we use the point-slope form:

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

Where \( m = 9 \), \( (x_1, y_1) = (-1, 6) \). Plugging these values in:

\[
y - 6 = 9(x + 1)
\]

Simplify:

\[
y - 6 = 9x + 9
\]

Add 6 to both sides:

\[
y = 9x + 15
\]

### Final Equation:
The equation of the line passing through the point \((-1, 6)\) with slope \( 9 \) is:

\[
y = 9x + 15
\]

Do you want further details or have any questions? 

Here are five related questions:
1. How do you find the slope of a line between two points?
2. What is the difference between point-slope form and slope-intercept form?
3. How do you determine if a point lies on a given line?
4. What are parallel lines, and how are their slopes related?
5. Can two different points yield the same slope for different lines?

**Tip:** Always check your work by plugging given points back into the final equation to ensure they satisfy the equation.

(-1,6);y=9x-5 write the equation in slope intercept form

Learn how to write the equation of a line in slope-intercept form given the point (-1, 6) and the equation y = 9x - 5. This step-by-step solution covers key algebraic concepts such as slope-intercept and point-slope forms. Ideal for Grades 8-10.

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