Question

A line passes through the points in this table.
x y
-24 0
-9 3
6 6
21 9
What is the slope of the line?
Write your answer as an integer or simplified fraction.

Answer
so what is it?
Answer
so 1/5 righ?
Answer
A line passes through the points in this table.
x y
44 63
46 43
48 23
50 3
What is the slope of the line?
Write your answer as an integer or simplified fraction.
Answer
A line passes through the points in this table.
x y
-12 17
2 11
16 5
30 -1
What is the slope of the line?
Write your answer as an integer or simplified fraction.

Answer
A line passes through the points in this table.
x y
1 11
3 7
4 5
6 1
What is the slope of the line?
Write your answer as an integer or simplified fraction.
Answered by GPT-4o mini
To find the slope of the line that passes through the given points, we can use the formula for slope \( m \):

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

We'll use the first two points from the table:

- Point 1: \((-24, 0)\) (where \(x_1 = -24\) and \(y_1 = 0\))
- Point 2: \((-9, 3)\) (where \(x_2 = -9\) and \(y_2 = 3\))

Now, let's substitute these values into the slope formula:

\[
m = \frac{3 - 0}{-9 - (-24)}
\]
\[
m = \frac{3}{-9 + 24}
\]
\[
m = \frac{3}{15}
\]
\[
m = \frac{1}{5}
\]

Now, let's double-check the slope using another set of points, say the points \((-9, 3)\) and \((6, 6)\):

- Point 1: \((-9, 3)\) (where \(x_1 = -9\) and \(y_1 = 3\))
- Point 2: \((6, 6)\) (where \(x_2 = 6\) and \(y_2 = 6\))

Now, calculating the slope again:

\[
m = \frac{6 - 3}{6 - (-9)}
\]
\[
m = \frac{3}{6 + 9}
\]
\[
m = \frac{3}{15}
\]
\[
m = \frac{1}{5}
\]

Lastly, using the points \((6, 6)\) and \((21, 9)\):

- Point 1: \((6, 6)\) (where \(x_1 = 6\) and \(y_1 = 6\))
- Point 2: \((21, 9)\) (where \(x_2 = 21\) and \(y_2 = 9\))

Calculating the slope again:

\[
m = \frac{9 - 6}{21 - 6}
\]
\[
m = \frac{3}{15} = \frac{1}{5}
\]

Since the slope is consistent across all pairs of points, we can conclude that the slope of the line is

\[
\boxed{\frac{1}{5}}
\]
Answered by GPT-4o mini
The slope of the line that passes through the points in the table is

\[
\boxed{\frac{1}{5}}.
\]
Answered by GPT-4o mini
Yes, that's correct! The slope of the line is \(\frac{1}{5}\).
Answered by GPT-4o mini
To find the slope of the line that passes through the given points, we will use the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's use the first two points from the table:

- Point 1: \((44, 63)\) (where \(x_1 = 44\) and \(y_1 = 63\))
- Point 2: \((46, 43)\) (where \(x_2 = 46\) and \(y_2 = 43\))

Now, we can calculate the slope:

\[
m = \frac{43 - 63}{46 - 44}
\]
\[
m = \frac{-20}{2}
\]
\[
m = -10
\]

Now let's double-check by calculating the slope using the points \((46, 43)\) and \((48, 23)\):

- Point 1: \((46, 43)\)
- Point 2: \((48, 23)\)

Calculating the slope again:

\[
m = \frac{23 - 43}{48 - 46}
\]
\[
m = \frac{-20}{2}
\]
\[
m = -10
\]

Finally, let's check the slope using the points \((48, 23)\) and \((50, 3)\):

- Point 1: \((48, 23)\)
- Point 2: \((50, 3)\)

Calculating the slope:

\[
m = \frac{3 - 23}{50 - 48}
\]
\[
m = \frac{-20}{2}
\]
\[
m = -10
\]

Since the slope is consistent across all pairs of points, we conclude that the slope of the line is

\[
\boxed{-10}.
\]
Answered by GPT-4o mini
To find the slope of the line that passes through the given points, we'll use the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's start by using the first two points from the table:

- Point 1: \((-12, 17)\) (where \(x_1 = -12\) and \(y_1 = 17\))
- Point 2: \((2, 11)\) (where \(x_2 = 2\) and \(y_2 = 11\))

Now we'll calculate the slope \(m\):

\[
m = \frac{11 - 17}{2 - (-12)}
\]
\[
m = \frac{-6}{2 + 12}
\]
\[
m = \frac{-6}{14}
\]
\[
m = \frac{-3}{7}
\]

Next, let's double-check the slope using the points \((2, 11)\) and \((16, 5)\):

- Point 1: \((2, 11)\)
- Point 2: \((16, 5)\)

Calculating the slope:

\[
m = \frac{5 - 11}{16 - 2}
\]
\[
m = \frac{-6}{14} = \frac{-3}{7}
\]

Finally, let's check the slope using the points \((16, 5)\) and \((30, -1)\):

- Point 1: \((16, 5)\)
- Point 2: \((30, -1)\)

Calculating the slope:

\[
m = \frac{-1 - 5}{30 - 16}
\]
\[
m = \frac{-6}{14} = \frac{-3}{7}
\]

Since the slope is consistent across all pairs of points, we conclude that the slope of the line is

\[
\boxed{\frac{-3}{7}}.
\]
Answered by GPT-4o mini
To find the slope of the line that passes through the given points, we will use the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's start by using the first two points from the table:

- Point 1: \((1, 11)\) (where \(x_1 = 1\) and \(y_1 = 11\))
- Point 2: \((3, 7)\) (where \(x_2 = 3\) and \(y_2 = 7\))

Now we'll calculate the slope \(m\):

\[
m = \frac{7 - 11}{3 - 1}
\]
\[
m = \frac{-4}{2}
\]
\[
m = -2
\]

Next, let's verify the slope using the next pair of points \((3, 7)\) and \((4, 5)\):

- Point 1: \((3, 7)\)
- Point 2: \((4, 5)\)

Calculating the slope:

\[
m = \frac{5 - 7}{4 - 3}
\]
\[
m = \frac{-2}{1}
\]
\[
m = -2
\]

Finally, let's check the slope using the points \((4, 5)\) and \((6, 1)\):

- Point 1: \((4, 5)\)
- Point 2: \((6, 1)\)

Calculating the slope:

\[
m = \frac{1 - 5}{6 - 4}
\]
\[
m = \frac{-4}{2}
\]
\[
m = -2
\]

Since the slope is consistent across all pairs of points, we conclude that the slope of the line is

\[
\boxed{-2}.
\]