To graph the equation $y + 7 = -\frac{1}{5}(x + 9)$, we first need to rewrite it in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Simplify the equation

Starting with:

$y + 7 = -\frac{1}{5}(x + 9)$

Distribute the $-\frac{1}{5}$ on the right-hand side:

$y + 7 = -\frac{1}{5}x - \frac{9}{5}$

Step 2: Isolate $y$

Subtract 7 from both sides:

$y = -\frac{1}{5}x - \frac{9}{5} - 7$

Convert 7 into a fraction with denominator 5:

$y = -\frac{1}{5}x - \frac{9}{5} - \frac{35}{5}$

Now combine the constant terms:

$y = -\frac{1}{5}x - \frac{44}{5}$

Step 3: Interpret the equation

Now the equation is in slope-intercept form:

$y = -\frac{1}{5}x - \frac{44}{5}$

• The slope ($m$) is $-\frac{1}{5}$.
• The y-intercept ($b$) is $-\frac{44}{5}$, or $-8.8$.

Step 4: Plot the graph

1. Start by plotting the y-intercept at $(0, -8.8)$.
2. Since the slope is $-\frac{1}{5}$, it means for every 5 units you move to the right along the x-axis, you move 1 unit down along the y-axis.

From the y-intercept, move right by 5 units (x = 5), and down by 1 unit (y = -9.8). Mark this point at $(5, -9.8)$.

You can then connect these points with a straight line, and extend it in both directions.

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Would you like more details on graphing, or have any further questions about this equation?

Here are some follow-up questions:

1. How do you find the x-intercept of this line?
2. What does the negative slope indicate about the line's direction?
3. Can you graph this equation using the point-slope form instead?
4. What is the equation in standard form (Ax + By = C)?
5. How do you graph a line with a positive slope?

Tip: When plotting lines with fractional slopes like $-\frac{1}{5}$, it's often easier to pick a few points by substituting values for $x$ and solving for $y$.