The given equation is $y = -6x + 4$. This is a linear equation in slope-intercept form, which follows the general pattern:

$y = mx + b$

where:

• $m$ is the slope.
• $b$ is the y-intercept (the value of $y$ when $x = 0$).

Key components:

1. Slope $m = -6$:

   • This means the line falls by 6 units for every 1 unit it moves to the right.

2. Y-intercept $b = 4$:

   • The line crosses the y-axis at $y = 4$.

Steps to Graph:

1. Plot the y-intercept:

   • Start by placing a point at $(0, 4)$ on the y-axis.

2. Use the slope to find another point:

   • From the y-intercept $(0, 4)$, move down 6 units and to the right 1 unit (since the slope is $-6 = -6/1$).
   • This gives the next point: $(1, -2)$.

3. Draw the line:

   • Connect the two points $(0, 4)$ and $(1, -2)$ with a straight line.

If you need the graph plotted visually, let me know! Alternatively, I can assist further with detailed explanations or adjustments.

Do you have any questions or want me to graph it for you?

Here are 5 related questions:

1. How do we determine if a line is increasing or decreasing based on its slope?
2. What happens to the line if the slope becomes steeper?
3. How can we rewrite the same equation in standard form $Ax + By = C$?
4. How do parallel lines relate in terms of slope?
5. What if the equation had been $y = -6x - 4$? Where would the y-intercept change?

Tip: To check your work, try finding one more point by substituting a different value for $x$ (e.g., $x = -1$) and verifying if it fits on the line.