Question

The pair of points (g, -1) and (2, 5) lie on a line with a slope of 3/2 what is the value of g?
A. 3
B. 4
C. -2
D. -5

Answer 1

To find the value of \( g \), we can use the formula for the slope of a line defined by two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

In this case, the points are \((g, -1)\) and \((2, 5)\). We can assign the points as follows:
- \( (x_1, y_1) = (g, -1) \)
- \( (x_2, y_2) = (2, 5) \)

Given that the slope is \(\frac{3}{2}\), we can set up the equation:

\[
\frac{5 - (-1)}{2 - g} = \frac{3}{2}
\]

This simplifies to:

\[
\frac{5 + 1}{2 - g} = \frac{3}{2}
\]

\[
\frac{6}{2 - g} = \frac{3}{2}
\]

Now, we can cross-multiply to solve for \( g \):

\[
6 \cdot 2 = 3 \cdot (2 - g)
\]

This simplifies to:

\[
12 = 6 - 3g
\]

Now, let's isolate \( g \):

\[
12 - 6 = -3g
\]

\[
6 = -3g
\]

Dividing both sides by -3 gives:

\[
g = -2
\]

Thus, the value of \( g \) is

\[
\boxed{-2}
\]

So the correct answer is C. -2.