write the equation in slope intercept form for the line with the given slope that contains the given point slope = -3; (-1,6)

The slope-intercept form of a line is:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept.

### Given:
- Slope \( m = -3 \)
- Point \( (-1, 6) \)

### Steps:

1. Substitute \( m = -3 \), \( x = -1 \), and \( y = 6 \) into the equation to solve for \( b \):

   \[
   6 = -3(-1) + b
   \]

2. Simplify:

   \[
   6 = 3 + b
   \]

3. Subtract 3 from both sides to solve for \( b \):

   \[
   b = 3
   \]

### Final Equation
The equation of the line in slope-intercept form is:

\[
y = -3x + 3
\]

Would you like a detailed breakdown of each step?

Here are five related questions:
1. How do you find the slope-intercept form if given two points instead of a slope and point?
2. What is the process to convert the slope-intercept form to the standard form?
3. How does the slope affect the angle of the line with respect to the x-axis?
4. How would the equation change if the line were parallel to this one?
5. What is the y-intercept and how can you graph this line?

**Tip:** Always check your slope and y-intercept values carefully to ensure they match the points given.

Write the equation in slope-intercept form for the line with the given slope that contains the given point: slope = -3; (-1,6)

Find the slope-intercept form equation of a line with a slope of -3 that passes through the point (-1, 6). This example demonstrates key algebraic concepts, including how to use the slope-intercept form formula to determine the y-intercept and construct the final equation. Suitable for students in Grades 8-10.

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