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Answer :
Let's find the slope for line [tex]\( l_2 \)[/tex] using the given points [tex]\((9, -1)\)[/tex] and [tex]\((8, -5)\)[/tex].
The formula for finding the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
For [tex]\( l_2 \)[/tex]:
- [tex]\( (x_1, y_1) = (9, -1) \)[/tex]
- [tex]\( (x_2, y_2) = (8, -5) \)[/tex]
Substitute these values into the slope formula:
[tex]\[ m = \frac{-5 - (-1)}{8 - 9} \][/tex]
[tex]\[ m = \frac{-5 + 1}{-1} \][/tex]
[tex]\[ m = \frac{-4}{-1} \][/tex]
[tex]\[ m = 4 \][/tex]
So, the slope of line [tex]\( l_2 \)[/tex] is [tex]\( 4 \)[/tex].
Now, for the analysis:
1. The slope of [tex]\( l_1 \)[/tex] is given as [tex]\( 0.25 \)[/tex].
2. The slope of [tex]\( l_2 \)[/tex] is [tex]\( 4 \)[/tex].
To determine if the lines are parallel, perpendicular, or neither:
- Lines are parallel if their slopes are equal.
- Lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex].
Let's check:
- Since [tex]\( 0.25 \)[/tex] is not equal to [tex]\( 4 \)[/tex], the lines are not parallel.
- To determine if they are perpendicular, calculate: [tex]\( 0.25 \times 4 = 1 \)[/tex], which is not [tex]\(-1\)[/tex].
Therefore, [tex]\( l_1 \)[/tex] and [tex]\( l_2 \)[/tex] are neither parallel nor perpendicular.
The formula for finding the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
For [tex]\( l_2 \)[/tex]:
- [tex]\( (x_1, y_1) = (9, -1) \)[/tex]
- [tex]\( (x_2, y_2) = (8, -5) \)[/tex]
Substitute these values into the slope formula:
[tex]\[ m = \frac{-5 - (-1)}{8 - 9} \][/tex]
[tex]\[ m = \frac{-5 + 1}{-1} \][/tex]
[tex]\[ m = \frac{-4}{-1} \][/tex]
[tex]\[ m = 4 \][/tex]
So, the slope of line [tex]\( l_2 \)[/tex] is [tex]\( 4 \)[/tex].
Now, for the analysis:
1. The slope of [tex]\( l_1 \)[/tex] is given as [tex]\( 0.25 \)[/tex].
2. The slope of [tex]\( l_2 \)[/tex] is [tex]\( 4 \)[/tex].
To determine if the lines are parallel, perpendicular, or neither:
- Lines are parallel if their slopes are equal.
- Lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex].
Let's check:
- Since [tex]\( 0.25 \)[/tex] is not equal to [tex]\( 4 \)[/tex], the lines are not parallel.
- To determine if they are perpendicular, calculate: [tex]\( 0.25 \times 4 = 1 \)[/tex], which is not [tex]\(-1\)[/tex].
Therefore, [tex]\( l_1 \)[/tex] and [tex]\( l_2 \)[/tex] are neither parallel nor perpendicular.
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