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.