Determine whether the lines through each pair of points are parallel, perpendicular, or neithe $$ \begin{array}{l}(9,4) \text { and }(3,5) \ (-3,-3) \text { and }(3,-4) \ \text { parallel } \ \text { perpendicular } \ \text { neither }\end{array} $$ Need Help?

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To determine whether the lines through each pair of points are parallel, perpendicular, or neither, we need to calculate the slopes of the lines formed by each pair of points.

The slope $$ m $$ of a line through two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is given by the formula:

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

### 1. For the points (9, 4) and (3, 5):

Let $$(x_1, y_1) = (9, 4)$$ and $$(x_2, y_2) = (3, 5)$$.

Calculating the slope:

$$
m_1 = \frac{5 - 4}{3 - 9} = \frac{1}{-6} = -\frac{1}{6}
$$

### 2. For the points (-3, -3) and (3, -4):

Let $$(x_1, y_1) = (-3, -3)$$ and $$(x_2, y_2) = (3, -4)$$.

Calculating the slope:

$$
m_2 = \frac{-4 - (-3)}{3 - (-3)} = \frac{-4 + 3}{3 + 3} = \frac{-1}{6}
$$

### Comparing the slopes:

- The slopes are $$ m_1 = -\frac{1}{6} $$ and $$ m_2 = -\frac{1}{6} $$.
- Since both slopes are equal, the lines are **parallel**.

### Conclusion:

The lines through the points (9, 4) and (3, 5) and the points (-3, -3) and (3, -4) are **parallel**.
The lines through the points (9, 4) and (3, 5) and the points (-3, -3) and (3, -4) are parallel.

Determine whether the lines through each pair of points are parallel, perpendicular, or neithe

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Determine whether the lines through each pair of points are parallel, perpendicular, or neithe Need Help?