Question

A line has a slope of 5 and includes the points (5,7) and (v,
–
3). What is the value of v?

Answer 1

To find the value of \( v \) for the line with a slope of 5 that includes the points \( (5, 7) \) and \( (v, -3) \), we can use the formula for the slope between 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, we can assign:
- \( (x_1, y_1) = (5, 7) \)
- \( (x_2, y_2) = (v, -3) \)

Given that the slope is 5, we can set up the equation:

\[
5 = \frac{-3 - 7}{v - 5}
\]

Simplifying the numerator gives:

\[
5 = \frac{-10}{v - 5}
\]

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

\[
5(v - 5) = -10
\]

Expanding the left side:

\[
5v - 25 = -10
\]

Next, add 25 to both sides:

\[
5v = 15
\]

Now, divide by 5:

\[
v = 3
\]

Thus, the value of \( v \) is

\[
\boxed{3}
\]