Question

The slope of line m is 5.

Which lines are parallel to line l?
Select each correct answer.
line p, which contains the points (6, 4) and (11, 3)
line q, which contains the points (3, 1) and (4, 6)
line k, which contains the points (4, 15) and (2, 5)
line n, which contains the points (3, 6) and (8,7)

Answer 1

To determine which lines are parallel to line l, we need to check if their slopes are equal.

Given that the slope of line m is 5, we can compare it with the slopes of the other lines:

line p: slope = (3 - 4) / (11 - 6) = -1 / 5
line q: slope = (6 - 1) / (4 - 3) = 5 / 1 = 5
line k: slope = (5 -15) / (2 - 4) = -10 / -2 = 5
line n: slope = (7 - 6) / (8 - 3) = 1 / 5

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Lines p, q, and k have a slope of 5, which is - 3) = the 5 / 1 = 5 same

Line k: Using the as the slope of line points (4, 15) and ( l.2, Therefore 5, lines p):
,slope = q, (5 and - k are15 parallel) / (2 to line l.

- So,4 the) correct = answers are: -10 / -2 line p, = 5 line q,

Line n: Using and line k. the points (3, 6) and (8, 7):
slope = (7 - 6) / (8 - 3) = 1 / 5 = 0.2

Now, comparing the slopes:

- Line p has a slope of -0.2, which is not equal to the slope of line m (5). Therefore, line p is not parallel to line l.

- Line q has a slope of 5, which is equal to the slope of line m (5). Therefore, line q is parallel to line l.

- Line k has a slope of 5, which is equal to the slope of line m (5). Therefore, line k is parallel to line l.

- Line n has a slope of 0.2, which is not equal to the slope of line m (5). Therefore, line n is not parallel to line l.

Based on the comparison of slopes, the correct answers are:

- Line q, which contains the points (3, 1) and (4, 6)
- Line k, which contains the points (4, 15) and (2, 5)

Answer 2

Answer: Lines q and k

Detailed explanation:

We're asked to find the slope of the line that's parallel to line m, given that m's slope is 5.

The important thing to realize is that parallel lines have equal slopes.

This means that if a line is parallel to line m, then it's going to have the same slope as line m.

Let's find the slope of each of these lines.

`\hrulefill`

LINE P

We're given that line p has the following points:
`\sf{(6,4)\:and\:(11,3)}`.

To find line p's slope I use the formula:

`\bf{m=(y_2-y_1)/(x_2-x_1)}`

Plug in the data:

`\bf{m=(3-4)/(11-6)=(-1)/(5)=-(1)/(5)}`

This line has a slope of -1/5, which is not equal to 5.

Therefore, line p is not parallel to line m.

`\hrulefill`

LINE Q

We're given that line q has the points
`\sf{(3,1)\:and\:(4,6)}`.

Once again, I use the slope formula:

`\bf{m=(6-1)/(4-3)=(5)/(1)=5}`

Since this line has a slope of 5, it's parallel to line m.

`\hrulefill`

LINE K

We know that line k contains the points (4,15) and (2,5).

`\bf{m=(5-15)/(2-4)=(-10)/(-2)=5}`

Line k is also parallel to line m.

`\hrulefill`

Finally, let's take a look at line n.

LINE N

We know that line n contains the points (3,6) and (8,7).

`\bf{m=(7-6)/(8-3)=(1)/(5)}`

Line n is not parallel to line m.

- - - - - - - - - - - - - - -

Therefore, the lines that are parallel to line m are: lines q and k.

Have a wonderful day! :)