To write the equation of a line in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept, we need to use the given slope and the point through which the line passes.

Given:

• Slope $m = -5$
• Point $(1, -9)$

We will substitute the point $(x_1, y_1) = (1, -9)$ and the slope $m = -5$ into the point-slope form equation:

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

Substitute the values:

$y - (-9) = -5(x - 1)$

Simplify the equation:

$y + 9 = -5(x - 1)$

Now distribute the $-5$:

$y + 9 = -5x + 5$

Next, isolate $y$ by subtracting 9 from both sides:

$y = -5x + 5 - 9$

Simplify the right-hand side:

$y = -5x - 4$

Thus, the equation of the line in slope-intercept form is:

$y = -5x - 4$

Do you want more details or have any questions?

Here are 5 questions to deepen understanding:

1. How would the equation change if the slope were positive instead of negative?
2. What is the significance of the slope in the equation?
3. How can we find the y-intercept algebraically from the point and slope?
4. How do you graph a line using slope-intercept form?
5. How would the equation change if the line passed through a different point?

Tip: Always check your final equation by substituting the given point back into the equation to ensure it satisfies the line equation!