The equation provided in the image is $4x + y = -1$. To graph this equation by plotting points, we can follow these steps:

Steps:

1. Rewrite the equation in slope-intercept form ($y = mx + b$): $y = -4x - 1$

   Here, the slope ($m$) is $-4$, and the y-intercept ($b$) is $-1$.

2. Find key points:

   • Start with $x = 0$:
     y = -4(0) - 1 = -1 \quad \text{(Point: (0, -1))}
   • Choose $x = 1$:
     y = -4(1) - 1 = -5 \quad \text{(Point: (1, -5))}
   • Choose $x = -1$:
     y = -4(-1) - 1 = 3 \quad \text{(Point: (-1, 3))}

3. Plot these points on the graph:

   • Plot $(0, -1)$, $(1, -5)$, and $(-1, 3)$.
   • Draw a straight line through these points to represent the equation.

Do you need help with graphing it further or additional clarification?

Related Questions:

1. What does the slope ($m = -4$) represent in this context?
2. How can we find the x-intercept of this equation?
3. How do we verify that a given point lies on the line?
4. What changes if the equation were $4x + y = 1$ instead?
5. Can you describe how the slope and y-intercept affect the shape of the line?

Tip:

To graph quickly, remember that the slope ($-4$) tells you the line decreases by 4 units in $y$ for every 1 unit increase in $x$.