Question

Math

Posted 4 months ago

```
What do the following two equations represent?
- $y-8=\frac{1}{2}(x+5)$
- $y-8=-\frac{1}{2}(x+5)$
Choose 1 answer:
(A) The same line
(B) Distinct parallel lines
(C) Perpendicular lines
(D) Intersecting, but not perpendicular lines
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 2

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept

step 3

The first equation $y - 8 = \frac{1}{2}(x + 5)$ can be rewritten as $y = \frac{1}{2}x + \frac{5}{2} + 8$

step 4

The second equation $y - 8 = -\frac{1}{2}(x + 5)$ can be rewritten as $y = -\frac{1}{2}x - \frac{5}{2} + 8$

step 5

Both equations have the same y-intercept, $8 + \frac{5}{2} = \frac{21}{2}$, but opposite slopes of $\frac{1}{2}$ and $-\frac{1}{2}$

step 6

Since the slopes are non-zero and negative reciprocals of each other, the lines are perpendicular

[1] Answer

C

Key Concept

Perpendicular Lines

Explanation

Two lines are perpendicular if their slopes are negative reciprocals of each other. In this case, the slopes are $\frac{1}{2}$ and $-\frac{1}{2}$, which are negative reciprocals.

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