To solve this, let's break the problem into parts.

Step 1: Find the slope of the given graphed line

The line that is graphed passes through two points: (-4, -6) and (8, 3). We need to first calculate the slope of this line using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where:

• $(x_1, y_1)$ = (-4, -6)
• $(x_2, y_2)$ = (8, 3)

$m = \frac{3 - (-6)}{8 - (-4)} = \frac{3 + 6}{8 + 4} = \frac{9}{12} = \frac{3}{4}$

The slope of the given graphed line is $\frac{3}{4}$.

Step 2: Identify the slope of the parallel line

The line we want to find passes through the point (8, -5) and is parallel to the given graphed line. Since parallel lines have the same slope, the slope of this line is also $\frac{3}{4}$.

Step 3: Use point-slope form to find the equation

Now, we'll use the point-slope form of a line equation, which is:

$y - y_1 = m(x - x_1)$

Substitute the point (8, -5) and the slope $\frac{3}{4}$ into this equation:

$y - (-5) = \frac{3}{4}(x - 8)$

Simplify:

$y + 5 = \frac{3}{4}(x - 8)$ $y + 5 = \frac{3}{4}x - 6$ $y = \frac{3}{4}x - 6 - 5$ $y = \frac{3}{4}x - 11$

Step 4: Compare with the options

The equation of the line is $y = \frac{3}{4}x - 11$, which matches option C.

Answer:

The correct answer is C. $y = \frac{3}{4}x - 11$.

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Would you like more details on any of these steps or clarification?

Here are 5 related questions to expand on this concept:

1. How do you find the equation of a line given two points?
2. What is the difference between the equations of parallel and perpendicular lines?
3. How do you find the y-intercept if only the slope and a point are given?
4. How do slopes affect the shape and steepness of a line?
5. How can you verify if two lines are parallel based on their equations?

Tip: When dealing with parallel lines, always remember that their slopes are identical.