Certainly! Let's analyze this step by step.

The equation given is:

$y = -4x + 4$

This is the equation of a straight line in slope-intercept form $y = mx + b$, where:

• $m$ is the slope, and
• $b$ is the y-intercept.

In this equation:

• The slope $m$ is $-4$. This means that for every 1 unit increase in $x$, $y$ decreases by 4 units (indicating a steep downward trend).
• The y-intercept $b$ is $4$. This tells us that the line crosses the y-axis at the point $(0, 4)$.

Steps to Graph this Line:

1. Plot the y-intercept (0, 4): From the graph, we can start at the point where $y = 4$ on the y-axis. This point is marked as the starting point.

2. Use the Slope to Find Another Point: The slope of $-4$ means we go down 4 units for every 1 unit we move to the right. Starting from $(0, 4)$:

   • Move 1 unit to the right to $x = 1$.
   • Move 4 units down to $y = 0$.
   • This brings us to the point $(1, 0)$.

3. Draw the Line: Once you have at least two points (like $(0, 4)$ and $(1, 0)$), you can draw a straight line through these points to represent the equation $y = -4x + 4$.

Red Segment

The red vertical line on the graph does not seem to represent the line $y = -4x + 4$. If it is supposed to illustrate a specific part of the line or mark an area of interest, please clarify. The actual line should be a continuous diagonal line crossing the y-axis at $y = 4$ and extending downwards to the right.

Would you like more details or have any specific questions?

Follow-Up Questions:

1. Would you like to see another example of using slope and y-intercept to graph a line?
2. Do you want to understand how to find the slope between two points?
3. Are you interested in learning more about slope-intercept form in general?
4. Would you like help with interpreting or identifying different forms of linear equations?
5. Do you need assistance with determining the slope of a line from its graph?

Tip:

For linear equations, remember that the y-intercept gives you a starting point on the y-axis, and the slope tells you the direction and steepness of the line.