Question

the slope of the line that passes through the points (-10,y)(5,2) is 2/5. what is the value of y

Answer 1

To find the value of \( y \) for the point \((-10, y)\) on the line that passes through the points \((-10, y)\) and \((5, 2)\) with a slope of \( \frac{2}{5} \), we can use the formula for the slope of a line given two points, which is:

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

Where:
- \( m \) is the slope
- \( (x_1, y_1) = (-10, y) \)
- \( (x_2, y_2) = (5, 2) \)

Substituting the values into the slope formula, we get:

\[
\frac{2}{5} = \frac{2 - y}{5 - (-10)}
\]

Simplifying the denominator:

\[
\frac{2}{5} = \frac{2 - y}{5 + 10} = \frac{2 - y}{15}
\]

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

\[
2 \cdot 15 = 5 \cdot (2 - y)
\]

This simplifies to:

\[
30 = 10 - 5y
\]

Now, isolate \( y \) by subtracting 10 from both sides:

\[
30 - 10 = -5y
\]

\[
20 = -5y
\]

Now, divide both sides by -5:

\[
y = \frac{20}{-5} = -4
\]

Thus, the value of \( y \) is:

\[
\boxed{-4}
\]