To graph the line given by the equation:

$y - 1 = -5(x + 4)$

we first rearrange it into slope-intercept form, $y = mx + b$.

Step 1: Distribute and Simplify

Rewrite the equation:

$y - 1 = -5(x + 4)$ $y - 1 = -5x - 20$

Now, add 1 to both sides to solve for $y$:

$y = -5x - 19$

This is now in the form $y = mx + b$, where the slope $m = -5$ and the y-intercept $b = -19$.

Step 2: Plot the Line

1. Identify the y-intercept: The y-intercept is at $(0, -19)$, which would be far down the graph. However, we can use the slope to find additional points that fall within the visible grid.

2. Use the Slope to Find Points: Since the slope $m = -5$, this means for every 1 unit you move to the right (increase in $x$), you move 5 units down (decrease in $y$).

3. Plot Points:

   • Start at a more manageable point such as $x = -4$, as this would simplify calculations within the visible grid.
   • When $x = -4$: $y = -5(-4) - 19 = 20 - 19 = 1$ So, one point on the line is $(-4, 1)$.
   • Using the slope, move one unit to the right to $x = -3$, and go down 5 units: $(-3, -4)$
   • Continue using this pattern if needed to plot further points.

You can now plot these points on the graph and draw a line through them to represent the equation $y - 1 = -5(x + 4)$.

Would you like further details on how to use these points, or do you have other questions?

Here are some questions that might deepen understanding:

1. How does changing the slope affect the steepness of the line?
2. What would happen if we changed the y-intercept value?
3. How can we find the x-intercept from this equation?
4. How does graphing with a positive slope differ from a negative one?
5. What does the equation tell us about the direction of the line?

Tip: When dealing with large intercepts that go off the grid, use the slope to find accessible points on the graph.