Question

A line with a slope of
3
8
passes through the points (
–
2,
–
1) and (
–
10,v). What is the value of v?
v=

Answer 1

To find the value of \( v \), we will use the formula for the slope of a line, which is defined as:

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

Here, we'll let \((x_1, y_1) = (-2, -1)\) and \((x_2, y_2) = (-10, v)\). Given that the slope \( m = \frac{3}{8} \), we can substitute the values into the slope formula:

\[
\frac{3}{8} = \frac{v - (-1)}{-10 - (-2)}
\]

Now, let's simplify the equation. The denominator becomes:

\[
-10 + 2 = -8
\]

So we have:

\[
\frac{3}{8} = \frac{v + 1}{-8}
\]

Next, we can cross-multiply to eliminate the fraction:

\[
3 \cdot (-8) = 8 \cdot (v + 1)
\]

This simplifies to:

\[
-24 = 8(v + 1)
\]

Now, distribute the 8 on the right side:

\[
-24 = 8v + 8
\]

Next, we can subtract 8 from both sides:

\[
-24 - 8 = 8v
\]

This gives us:

\[
-32 = 8v
\]

Now, divide both sides by 8:

\[
v = \frac{-32}{8}
\]

Simplifying this gives:

\[
v = -4
\]

Thus, the value of \( v \) is

\[
\boxed{-4}
\]