The given equation is:

$y - 4 = -2(x - 1)$

Let's rewrite this equation into slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. Distribute the $-2$ on the right-hand side:

$y - 4 = -2x + 2$

2. Add 4 to both sides to isolate $y$:

$y = -2x + 6$

Now the equation is in slope-intercept form: $y = -2x + 6$.

Graphing:

• The slope $m = -2$, meaning the line decreases by 2 units in $y$ for every 1 unit increase in $x$.
• The y-intercept $b = 6$, which means the line crosses the y-axis at $(0, 6)$.

Steps for graphing:

1. Plot the y-intercept at $(0, 6)$.
2. Use the slope $-2$ (which can be written as $\frac{-2}{1}$) to move down 2 units in $y$ and 1 unit to the right in $x$.
3. Draw the line through these points.

Would you like further clarification or details on how to graph this? Here are five related questions you might consider:

1. How do you calculate the slope between two points?
2. How does changing the slope affect the graph of a line?
3. What happens when you change the y-intercept in a linear equation?
4. How do you find the equation of a line given two points?
5. How can you check if a point lies on a given line?

Tip: When graphing a linear equation, always check the slope direction (positive/negative) to ensure the line tilts correctly!