The given equation is:

$x + 4y = -8$

To graph this linear equation, it's helpful to convert it to slope-intercept form ($y = mx + b$), where $m$ is the slope and $b$ is the y-intercept.

Step 1: Solve for $y$

Start by isolating $y$ on one side of the equation.

$x + 4y = -8$ Subtract $x$ from both sides:

$4y = -x - 8$ Now, divide both sides by 4:

$y = -\frac{1}{4}x - 2$

Step 2: Identify the slope and y-intercept

• The slope ($m$) is $-\frac{1}{4}$, meaning the line goes down 1 unit for every 4 units it moves to the right.
• The y-intercept ($b$) is $-2$, meaning the line crosses the y-axis at $(0, -2)$.

Step 3: Plotting the line

1. Start by plotting the y-intercept $(0, -2)$.
2. Use the slope $-\frac{1}{4}$ to find another point. From $(0, -2)$, move right 4 units (positive direction on the x-axis) and move down 1 unit (negative direction on the y-axis) to get the point $(4, -3)$.
3. Draw a straight line through the points $(0, -2)$ and $(4, -3)$.

Would you like me to provide the graph as well? Let me know if you'd like further details or if you have questions!

Here are some related questions:

1. How can you find the x-intercept of a linear equation?
2. What does the slope of a line represent geometrically?
3. How do you graph a line if you are given two points?
4. How do you convert a standard form equation to slope-intercept form?
5. What is the significance of a negative slope in a linear equation?

Tip: Always try to find both intercepts (x and y) for better accuracy when graphing lines.