Question

The pair of points (g, -1) and (2, 5) lie on a line with a slope of 32
. What is the value of g? (1 point)
Responses

-2
-2

4
4

-5
-5

3

Find the slope of a line that passes through (–10, –1) and (5, - 4).(1 point)
Responses

1
1

-3
-3

−1/5
negative 1 fifth

1/3

Answer 1

To find the value of \( g \) given the points \( (g, -1) \) and \( (2, 5) \) with a slope of 32, we can use the slope formula:

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

where \( m \) is the slope, \( (x_1, y_1) \) is the first point, and \( (x_2, y_2) \) is the second point.

Substituting the points we have:
- \( (x_1, y_1) = (g, -1) \)
- \( (x_2, y_2) = (2, 5) \)

Setting the slope \( m = 32 \):

\[
32 = \frac{5 - (-1)}{2 - g}
\]

This simplifies to:

\[
32 = \frac{5 + 1}{2 - g}
\]
\[
32 = \frac{6}{2 - g}
\]

Now, we can cross-multiply:

\[
32(2 - g) = 6
\]
\[
64 - 32g = 6
\]
\[
64 - 6 = 32g
\]
\[
58 = 32g
\]
\[
g = \frac{58}{32} = \frac{29}{16}
\]

Now, we also need to find the slope of the line that passes through the points \( (-10, -1) \) and \( (5, -4) \).

Using the slope formula again:

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

Substituting the points:
- \( (x_1, y_1) = (-10, -1) \)
- \( (x_2, y_2) = (5, -4) \)

So we have:

\[
m = \frac{-4 - (-1)}{5 - (-10)} = \frac{-4 + 1}{5 + 10} = \frac{-3}{15} = -\frac{1}{5}
\]

So, the answers are:
1. The value of \( g \) is not among the provided options as it calculates to \( \frac{29}{16} \).
2. The slope of the line that passes through \( (-10, -1) \) and \( (5, -4) \) is \( -\frac{1}{5} \).