To graph the equation $y - 1 = -2(x + 1)$, let's first rewrite it in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Simplify the equation

Starting with: $y - 1 = -2(x + 1)$ Distribute the $-2$ on the right-hand side: $y - 1 = -2x - 2$ Now, add 1 to both sides to solve for $y$: $y = -2x - 1$

Step 2: Identify the slope and y-intercept

The equation is now in the form $y = mx + b$, where:

• Slope $m = -2$
• Y-intercept $b = -1$

This means the line has a slope of -2 (it falls 2 units for every 1 unit moved to the right) and crosses the y-axis at $y = -1$.

Step 3: Graph the line

1. Start at the y-intercept: point $(0, -1)$.
2. From this point, use the slope $-2$ to find another point: move down 2 units and right 1 unit, landing at $(1, -3)$.
3. Connect these two points with a straight line.

Would you like a visual of the graph, or any additional details on how to interpret the slope or intercept?

Here are 5 related questions to explore further:

1. How do you interpret the slope of a line geometrically?
2. How does changing the slope of the line affect its steepness?
3. What happens if the y-intercept is positive or zero?
4. How do you graph a line from an equation in point-slope form?
5. How do you find the x-intercept of a line?

Tip: If the slope is negative, the line will slope downward as you move from left to right across the graph.