To graph the equation $y + 7 = -\frac{1}{5}(x + 9)$, let's first rewrite it into slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Simplify the equation

Starting with: $y + 7 = -\frac{1}{5}(x + 9)$ First, distribute $-\frac{1}{5}$ to both terms inside the parentheses: $y + 7 = -\frac{1}{5}x - \frac{9}{5}$

Step 2: Isolate $y$

Now, subtract 7 from both sides to solve for $y$: $y = -\frac{1}{5}x - \frac{9}{5} - 7$ Convert $7$ into a fraction with denominator 5: $y = -\frac{1}{5}x - \frac{9}{5} - \frac{35}{5}$ Now combine the constants: $y = -\frac{1}{5}x - \frac{44}{5}$

Step 3: Identify the slope and y-intercept

The equation is now in the form $y = mx + b$, where:

• Slope $m = -\frac{1}{5}$
• y-intercept $b = -\frac{44}{5}$

Step 4: Graphing

• The y-intercept is $-\frac{44}{5}$ or $-8.8$. This means the line crosses the y-axis at $(0, -8.8)$.
• The slope is $-\frac{1}{5}$, meaning for every 5 units you move to the right (along the x-axis), you move 1 unit down (along the y-axis).

To plot the line:

1. Start at the point $(0, -8.8)$.
2. From there, move 5 units to the right and 1 unit down to plot the next point.
3. Draw a straight line through the points.

Let me know if you'd like more details or have any questions!

Related Questions:

1. How do you find the slope and y-intercept from a linear equation in standard form?
2. How do you graph a line when the slope is negative?
3. How do you convert an equation from point-slope form to slope-intercept form?
4. What does the slope of a line represent in a real-world context?
5. How can you verify that two lines are parallel or perpendicular?

Tip:

When graphing a line, it's often helpful to identify two points first, as this makes it easier to plot the line accurately.