

What is the equation of a line that passes through (8,-5) and is parallel to the graphed line?

In a linear graph line diagram, A line passes through (minus 4, minus 6) and (8, 3) which intersects the x-axis at 4 units and the y-axis at minus 3 units.
A.y = -4/3x - 47/3
B.y = 3/4x + 1
C.y = 3/4x -11
D.y = -3/4x + 17/3


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.

What is the equation of a line that passes through (8,-5) and is parallel to the graphed line?

In a linear graph line diagram, a line passes through (-4, -6) and (8, 3) which intersects the x-axis at 4 units and the y-axis at -3 units.
A.y = -4/3x - 47/3
B.y = 3/4x + 1
C.y = 3/4x -11
D.y = -3/4x + 17/3

Learn how to find the equation of a line that passes through the point (8,-5) and is parallel to a line passing through (-4,-6) and (8,3). This problem focuses on slope calculations, point-slope form, and properties of parallel lines. Suitable for Grades 8-10.

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