Question

the slope of the line that passes through the points (-2,y) and (-5,7) is -2/3. what is the value of y?

Answer 1

To find the value of \( y \) for the points \((-2, y)\) and \((-5, 7)\) with a slope of \(-\frac{2}{3}\), we can use the formula for the slope of a line given by the coordinates of two points, which is:

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

Here, we can identify the coordinates as follows:
- \( (x_1, y_1) = (-2, y) \)
- \( (x_2, y_2) = (-5, 7) \)

Substituting these points into the slope formula:

\[
-\frac{2}{3} = \frac{7 - y}{-5 - (-2)}
\]

Now simplify the denominator:

\[
-5 - (-2) = -5 + 2 = -3
\]

Thus, the equation becomes:

\[
-\frac{2}{3} = \frac{7 - y}{-3}
\]

Now, to eliminate the fraction, we can multiply both sides by -3:

\[
-3 \cdot \left(-\frac{2}{3}\right) = 7 - y
\]

This simplifies to:

\[
2 = 7 - y
\]

Next, isolate \( y \) by rearranging the equation:

\[
y = 7 - 2
\]
\[
y = 5
\]

Thus, the value of \( y \) is \( \boxed{5} \).