which statement is true about the graph of the line 8x + 3y = 0? a. it is a vertical line   b. it is a horizontal line.  c. it passes through (8, 3).   d. it passes through the origin

We are given the equation of a line: 

\[
8x + 3y = 0
\]

To better understand the line, let's rewrite the equation in slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

1. Solve for \(y\):
   \[
   3y = -8x
   \]
   \[
   y = -\frac{8}{3}x
   \]

Now we can analyze the line:

- The slope of the line is \(-\frac{8}{3}\), which means it is neither vertical nor horizontal (this rules out options a and b).
- The y-intercept (\(b\)) is 0, which means the line passes through the origin, \((0, 0)\) (this confirms option d is correct).
- To check option c, substitute \(x = 8\) and \(y = 3\) into the original equation:
  \[
  8(8) + 3(3) = 64 + 9 = 73 \neq 0
  \]
  Therefore, the point \((8, 3)\) does not lie on the line (this rules out option c).

**Answer: d. It passes through the origin.**

Would you like further details or have any questions?

Here are 5 related questions:
1. How can we determine if a line is vertical or horizontal from its equation?
2. How do you find the slope of a line given its equation?
3. How can you determine if a point lies on a given line?
4. What is the significance of the slope in the slope-intercept form?
5. How do you graph a line given its slope and intercept?

**Tip:** For any linear equation, the constant term in standard form (\(Ax + By = C\)) helps determine if the line passes through the origin.

Which statement is true about the graph of the line 8x + 3y = 0? a. it is a vertical line b. it is a horizontal line. c. it passes through (8, 3). d. it passes through the origin.

Analyze the line 8x + 3y = 0 to determine its properties. This problem explores concepts in algebra, including converting to slope-intercept form and checking if the line passes through specific points. Suitable for students in Grades 8-10.

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