Question

Find the slope of the line that passes through the points given in then first column and choose the correct result.
Points
4
4
−
2
3
3
−2
​

5
8
8
5
​

(
1
,
4
)

a
n
d

(
−
1
,
−
4
)
(1,4) and (−1,−4)



(
−
3
,
3
)

a
n
d

(
3
,
−
1
)
(−3,3) and (3,−1)



(
8
,
4
)

a
n
d

(
0
,
−
1
)
(8,4) and (0,−1)

Answer 1

To find the slope of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\), you can use the formula:

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

Let's calculate the slope for each pair of points provided.

1. **Points (1, 4) and (-1, -4)**:
- Here, \((x_1, y_1) = (1, 4)\) and \((x_2, y_2) = (-1, -4)\).
- Slope:
\[
\text{slope} = \frac{-4 - 4}{-1 - 1} = \frac{-8}{-2} = 4
\]

2. **Points (-3, 3) and (3, -1)**:
- Here, \((x_1, y_1) = (-3, 3)\) and \((x_2, y_2) = (3, -1)\).
- Slope:
\[
\text{slope} = \frac{-1 - 3}{3 - (-3)} = \frac{-4}{6} = -\frac{2}{3}
\]

3. **Points (8, 4) and (0, -1)**:
- Here, \((x_1, y_1) = (8, 4)\) and \((x_2, y_2) = (0, -1)\).
- Slope:
\[
\text{slope} = \frac{-1 - 4}{0 - 8} = \frac{-5}{-8} = \frac{5}{8}
\]

### Summary of Results:
1. Slope between (1, 4) and (-1, -4) is **4**.
2. Slope between (-3, 3) and (3, -1) is **-\frac{2}{3}**.
3. Slope between (8, 4) and (0, -1) is **\frac{5}{8}**.