The equation provided in the image is:

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

We will convert this to slope-intercept form $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept.

Step 1: Distribute the $-4$ on the right-hand side

$y - 2 = -4(x - 1) \implies y - 2 = -4x + 4$

Step 2: Add 2 to both sides to solve for $y$

$y = -4x + 4 + 2 \implies y = -4x + 6$

Now, the equation is in slope-intercept form:

$y = -4x + 6$

• Slope (m): -4
• Y-intercept (b): 6

Graphing:

1. Start by plotting the y-intercept, which is the point $(0, 6)$.
2. Use the slope $-4$, which means "down 4 units for every 1 unit to the right," to plot the next points.

Example Points:

• From $(0, 6)$, move down 4 units and right 1 unit to plot the point $(1, 2)$.
• Repeat to plot other points like $(2, -2)$, $(3, -6)$, and so on.

Once the points are plotted, draw a straight line through them to represent the equation $y = -4x + 6$.

Do you need more details or have any other questions?

Here are 5 related questions to consider:

1. How do you interpret the slope of a line in real-world problems?
2. What happens to the graph if the slope changes but the y-intercept stays the same?
3. Can you graph a line without first converting to slope-intercept form?
4. What are other forms of linear equations besides slope-intercept form?
5. How do you find the equation of a line given two points?

Tip: Always check the direction of the slope. A negative slope means the line goes downward from left to right!