To write the equation of the line that passes through the point $(3, -3)$ with a slope $m = 3$, we can use the point-slope form of a line, which is:

$y - y_1 = m(x - x_1)$

where $(x_1, y_1)$ is the given point and $m$ is the slope.

Given:

• $m = 3$
• $(x_1, y_1) = (3, -3)$

Substituting these values into the point-slope form:

$y - (-3) = 3(x - 3)$

Simplifying:

$y + 3 = 3(x - 3)$

Distribute the slope on the right side:

$y + 3 = 3x - 9$

Now, subtract 3 from both sides to solve for $y$:

$y = 3x - 9 - 3$

$y = 3x - 12$

Thus, the equation of the line is:

$y = 3x - 12$

So the values are:

• $m = 3$ (slope)
• $b = -12$ (y-intercept)

Would you like further clarification or additional details? Here are five related questions to deepen understanding:

1. How do you convert from point-slope form to slope-intercept form?
2. What would the equation be if the slope were negative?
3. How can you verify the equation is correct using the point provided?
4. How do you graph a line given its slope and y-intercept?
5. How does the slope affect the steepness of the line?

Tip: When graphing a line, always plot the y-intercept first, and then use the slope to find additional points.